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Rep:Sb6014 TS 2017

2017-11-10T17:29:54Z

Sb6014: /* Thermodynamic data */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement.

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

Method 2 was used to locate the transition state and determine the IRC for this reaction.

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermodynamic data ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |(kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

Method 3 was used to locate the transition state and determine the IRC for this reaction.

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

===Thermodynamic data ===

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
! colspan="3" |(kJ/mol)
|-
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== Conclusion ==

Computational methods were used to identify the transition state of various reactions. Thermodynamic data was also extracted, and the kinetic and thermodynamic data products were determined. The limitations of such methods was also discussed, and improvements to further investigations were also suggested.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

==Log files ==
{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3e/DIENE_OPTPM6_%282.2%29.LOG file]
|-
|Alkene
|[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/ALKENE_OPTPM6_%282%29.LOG file]
|-
|TS
|[https://wiki.ch.ic.ac.uk/wiki/images/1/13/EX1_TSOPTPM6.LOG file]
|-
|Products
|[https://wiki.ch.ic.ac.uk/wiki/images/7/72/EX1_OPTPRODUCTPM6.LOG file]
|-
|IRC
|[https://wiki.ch.ic.ac.uk/wiki/images/8/85/EX1_IRCPM6.LOG file]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_HEXADIENEOPTPM6%282%29.LOG file]
|-
|Dioxole
|[https://wiki.ch.ic.ac.uk/wiki/images/5/52/EX2_OPTDIOXOLEPM6.LOG file]
|-
|TS Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/a/a5/EX2_TSOPTPM6_EXO.LOG file]
|-
|TS Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/55/EX2_TSB3_EXO.LOG file]
|-
|Product Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_PRODUCT_B3_EXO.LOG file]
|-
|IRC Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9d/EX2_TSIRCPM6_EXO.LOG file]
|-
|TS Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4a/EX2_TSPM6_ENDO.LOG file]
|-
|TS Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/57/EX2_TSB3_ENDO.LOG file]
|-
|Product Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/0/03/EX2_PRODUCTOPT_ENDO.LOG file]
|-
|IRC Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e0/EX2_IRCPM6_ENDO.LOG file]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3d/EX3_XYLYLENE_OPT.LOG file]
|-
|SO<sub>2</sub>
|[https://wiki.ch.ic.ac.uk/wiki/images/9/97/EX3_SO2_REOPT.LOG file]
|-
|TS DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/EX3_TS_EXO.LOG file]
|-
|Product DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9f/EX3_PRODUCTOPTPM6_EXO.LOG file]
|-
|IRC DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/93/EX3_IRC_DA_EXO.LOG file]
|-
|TS DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/7/7a/EX3_TS_DA_ENDO.LOG file]
|-
|Product DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/8/87/EX3_PRODUCTOPT_ENDO.LOG file]
|-
|IRC DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f6/EX3_IRC_DA_ENDO.LOG file]
|-
|TS Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/3/37/EX3_CT_TS.LOG file]
|-
|Product Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4c/EX3_CT_PRODUCTOPT.LOG file]
|-
|IRC Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e6/EX3_CT_IRC.LOG file]
|}

Rep:Sb6014 TS 2017

2017-11-10T17:29:27Z

Sb6014: /* Thermodynamic data */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement.

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

Method 2 was used to locate the transition state and determine the IRC for this reaction.

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermodynamic data ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |(kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

Method 3 was used to locate the transition state and determine the IRC for this reaction.

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

===Thermodynamic data ===

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
| colspan="3" | kJ/mol
|-
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== Conclusion ==

Computational methods were used to identify the transition state of various reactions. Thermodynamic data was also extracted, and the kinetic and thermodynamic data products were determined. The limitations of such methods was also discussed, and improvements to further investigations were also suggested.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

==Log files ==
{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3e/DIENE_OPTPM6_%282.2%29.LOG file]
|-
|Alkene
|[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/ALKENE_OPTPM6_%282%29.LOG file]
|-
|TS
|[https://wiki.ch.ic.ac.uk/wiki/images/1/13/EX1_TSOPTPM6.LOG file]
|-
|Products
|[https://wiki.ch.ic.ac.uk/wiki/images/7/72/EX1_OPTPRODUCTPM6.LOG file]
|-
|IRC
|[https://wiki.ch.ic.ac.uk/wiki/images/8/85/EX1_IRCPM6.LOG file]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_HEXADIENEOPTPM6%282%29.LOG file]
|-
|Dioxole
|[https://wiki.ch.ic.ac.uk/wiki/images/5/52/EX2_OPTDIOXOLEPM6.LOG file]
|-
|TS Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/a/a5/EX2_TSOPTPM6_EXO.LOG file]
|-
|TS Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/55/EX2_TSB3_EXO.LOG file]
|-
|Product Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_PRODUCT_B3_EXO.LOG file]
|-
|IRC Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9d/EX2_TSIRCPM6_EXO.LOG file]
|-
|TS Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4a/EX2_TSPM6_ENDO.LOG file]
|-
|TS Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/57/EX2_TSB3_ENDO.LOG file]
|-
|Product Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/0/03/EX2_PRODUCTOPT_ENDO.LOG file]
|-
|IRC Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e0/EX2_IRCPM6_ENDO.LOG file]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3d/EX3_XYLYLENE_OPT.LOG file]
|-
|SO<sub>2</sub>
|[https://wiki.ch.ic.ac.uk/wiki/images/9/97/EX3_SO2_REOPT.LOG file]
|-
|TS DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/EX3_TS_EXO.LOG file]
|-
|Product DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9f/EX3_PRODUCTOPTPM6_EXO.LOG file]
|-
|IRC DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/93/EX3_IRC_DA_EXO.LOG file]
|-
|TS DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/7/7a/EX3_TS_DA_ENDO.LOG file]
|-
|Product DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/8/87/EX3_PRODUCTOPT_ENDO.LOG file]
|-
|IRC DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f6/EX3_IRC_DA_ENDO.LOG file]
|-
|TS Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/3/37/EX3_CT_TS.LOG file]
|-
|Product Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4c/EX3_CT_PRODUCTOPT.LOG file]
|-
|IRC Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e6/EX3_CT_IRC.LOG file]
|}

Rep:Sb6014 TS 2017

2017-11-10T17:27:39Z

Sb6014: /* Thermodynamic data */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement.

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

Method 2 was used to locate the transition state and determine the IRC for this reaction.

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermodynamic data ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

Method 3 was used to locate the transition state and determine the IRC for this reaction.

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

===Thermodynamic data ===

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
| colspan="3" | kJ/mol
|-
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== Conclusion ==

Computational methods were used to identify the transition state of various reactions. Thermodynamic data was also extracted, and the kinetic and thermodynamic data products were determined. The limitations of such methods was also discussed, and improvements to further investigations were also suggested.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

==Log files ==
{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3e/DIENE_OPTPM6_%282.2%29.LOG file]
|-
|Alkene
|[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/ALKENE_OPTPM6_%282%29.LOG file]
|-
|TS
|[https://wiki.ch.ic.ac.uk/wiki/images/1/13/EX1_TSOPTPM6.LOG file]
|-
|Products
|[https://wiki.ch.ic.ac.uk/wiki/images/7/72/EX1_OPTPRODUCTPM6.LOG file]
|-
|IRC
|[https://wiki.ch.ic.ac.uk/wiki/images/8/85/EX1_IRCPM6.LOG file]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_HEXADIENEOPTPM6%282%29.LOG file]
|-
|Dioxole
|[https://wiki.ch.ic.ac.uk/wiki/images/5/52/EX2_OPTDIOXOLEPM6.LOG file]
|-
|TS Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/a/a5/EX2_TSOPTPM6_EXO.LOG file]
|-
|TS Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/55/EX2_TSB3_EXO.LOG file]
|-
|Product Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_PRODUCT_B3_EXO.LOG file]
|-
|IRC Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9d/EX2_TSIRCPM6_EXO.LOG file]
|-
|TS Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4a/EX2_TSPM6_ENDO.LOG file]
|-
|TS Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/57/EX2_TSB3_ENDO.LOG file]
|-
|Product Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/0/03/EX2_PRODUCTOPT_ENDO.LOG file]
|-
|IRC Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e0/EX2_IRCPM6_ENDO.LOG file]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3d/EX3_XYLYLENE_OPT.LOG file]
|-
|SO<sub>2</sub>
|[https://wiki.ch.ic.ac.uk/wiki/images/9/97/EX3_SO2_REOPT.LOG file]
|-
|TS DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/EX3_TS_EXO.LOG file]
|-
|Product DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9f/EX3_PRODUCTOPTPM6_EXO.LOG file]
|-
|IRC DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/93/EX3_IRC_DA_EXO.LOG file]
|-
|TS DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/7/7a/EX3_TS_DA_ENDO.LOG file]
|-
|Product DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/8/87/EX3_PRODUCTOPT_ENDO.LOG file]
|-
|IRC DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f6/EX3_IRC_DA_ENDO.LOG file]
|-
|TS Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/3/37/EX3_CT_TS.LOG file]
|-
|Product Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4c/EX3_CT_PRODUCTOPT.LOG file]
|-
|IRC Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e6/EX3_CT_IRC.LOG file]
|}

Rep:Sb6014 TS 2017

2017-11-10T17:26:39Z

Sb6014: /* Thermodynamic data */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement.

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

Method 2 was used to locate the transition state and determine the IRC for this reaction.

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermodynamic data ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

Method 3 was used to locate the transition state and determine the IRC for this reaction.

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

===Thermodynamic data ===

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
| colspan ="3" !kJ/mol
|-
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== Conclusion ==

Computational methods were used to identify the transition state of various reactions. Thermodynamic data was also extracted, and the kinetic and thermodynamic data products were determined. The limitations of such methods was also discussed, and improvements to further investigations were also suggested.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

==Log files ==
{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3e/DIENE_OPTPM6_%282.2%29.LOG file]
|-
|Alkene
|[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/ALKENE_OPTPM6_%282%29.LOG file]
|-
|TS
|[https://wiki.ch.ic.ac.uk/wiki/images/1/13/EX1_TSOPTPM6.LOG file]
|-
|Products
|[https://wiki.ch.ic.ac.uk/wiki/images/7/72/EX1_OPTPRODUCTPM6.LOG file]
|-
|IRC
|[https://wiki.ch.ic.ac.uk/wiki/images/8/85/EX1_IRCPM6.LOG file]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_HEXADIENEOPTPM6%282%29.LOG file]
|-
|Dioxole
|[https://wiki.ch.ic.ac.uk/wiki/images/5/52/EX2_OPTDIOXOLEPM6.LOG file]
|-
|TS Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/a/a5/EX2_TSOPTPM6_EXO.LOG file]
|-
|TS Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/55/EX2_TSB3_EXO.LOG file]
|-
|Product Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_PRODUCT_B3_EXO.LOG file]
|-
|IRC Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9d/EX2_TSIRCPM6_EXO.LOG file]
|-
|TS Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4a/EX2_TSPM6_ENDO.LOG file]
|-
|TS Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/57/EX2_TSB3_ENDO.LOG file]
|-
|Product Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/0/03/EX2_PRODUCTOPT_ENDO.LOG file]
|-
|IRC Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e0/EX2_IRCPM6_ENDO.LOG file]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3d/EX3_XYLYLENE_OPT.LOG file]
|-
|SO<sub>2</sub>
|[https://wiki.ch.ic.ac.uk/wiki/images/9/97/EX3_SO2_REOPT.LOG file]
|-
|TS DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/EX3_TS_EXO.LOG file]
|-
|Product DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9f/EX3_PRODUCTOPTPM6_EXO.LOG file]
|-
|IRC DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/93/EX3_IRC_DA_EXO.LOG file]
|-
|TS DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/7/7a/EX3_TS_DA_ENDO.LOG file]
|-
|Product DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/8/87/EX3_PRODUCTOPT_ENDO.LOG file]
|-
|IRC DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f6/EX3_IRC_DA_ENDO.LOG file]
|-
|TS Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/3/37/EX3_CT_TS.LOG file]
|-
|Product Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4c/EX3_CT_PRODUCTOPT.LOG file]
|-
|IRC Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e6/EX3_CT_IRC.LOG file]
|}

Rep:Sb6014 TS 2017

2017-11-10T17:20:09Z

Sb6014: /* Log files */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement.

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

Method 2 was used to locate the transition state and determine the IRC for this reaction.

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermodynamic data ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

Method 3 was used to locate the transition state and determine the IRC for this reaction.

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

===Thermodynamic data ===

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== Conclusion ==

Computational methods were used to identify the transition state of various reactions. Thermodynamic data was also extracted, and the kinetic and thermodynamic data products were determined. The limitations of such methods was also discussed, and improvements to further investigations were also suggested.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

==Log files ==
{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3e/DIENE_OPTPM6_%282.2%29.LOG file]
|-
|Alkene
|[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/ALKENE_OPTPM6_%282%29.LOG file]
|-
|TS
|[https://wiki.ch.ic.ac.uk/wiki/images/1/13/EX1_TSOPTPM6.LOG file]
|-
|Products
|[https://wiki.ch.ic.ac.uk/wiki/images/7/72/EX1_OPTPRODUCTPM6.LOG file]
|-
|IRC
|[https://wiki.ch.ic.ac.uk/wiki/images/8/85/EX1_IRCPM6.LOG file]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_HEXADIENEOPTPM6%282%29.LOG file]
|-
|Dioxole
|[https://wiki.ch.ic.ac.uk/wiki/images/5/52/EX2_OPTDIOXOLEPM6.LOG file]
|-
|TS Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/a/a5/EX2_TSOPTPM6_EXO.LOG file]
|-
|TS Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/55/EX2_TSB3_EXO.LOG file]
|-
|Product Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_PRODUCT_B3_EXO.LOG file]
|-
|IRC Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9d/EX2_TSIRCPM6_EXO.LOG file]
|-
|TS Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4a/EX2_TSPM6_ENDO.LOG file]
|-
|TS Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/57/EX2_TSB3_ENDO.LOG file]
|-
|Product Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/0/03/EX2_PRODUCTOPT_ENDO.LOG file]
|-
|IRC Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e0/EX2_IRCPM6_ENDO.LOG file]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3d/EX3_XYLYLENE_OPT.LOG file]
|-
|SO<sub>2</sub>
|[https://wiki.ch.ic.ac.uk/wiki/images/9/97/EX3_SO2_REOPT.LOG file]
|-
|TS DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/EX3_TS_EXO.LOG file]
|-
|Product DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9f/EX3_PRODUCTOPTPM6_EXO.LOG file]
|-
|IRC DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/93/EX3_IRC_DA_EXO.LOG file]
|-
|TS DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/7/7a/EX3_TS_DA_ENDO.LOG file]
|-
|Product DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/8/87/EX3_PRODUCTOPT_ENDO.LOG file]
|-
|IRC DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f6/EX3_IRC_DA_ENDO.LOG file]
|-
|TS Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/3/37/EX3_CT_TS.LOG file]
|-
|Product Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4c/EX3_CT_PRODUCTOPT.LOG file]
|-
|IRC Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e6/EX3_CT_IRC.LOG file]
|}

Thermochemdatasb6014

2017-11-10T17:19:46Z

Sb6014: /* eX 2 */

==eX 2==

{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3e/DIENE_OPTPM6_%282.2%29.LOG file]
|-
|Alkene
|[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/ALKENE_OPTPM6_%282%29.LOG file]
|-
|TS
|[https://wiki.ch.ic.ac.uk/wiki/images/1/13/EX1_TSOPTPM6.LOG file]
|-
|Products
|[https://wiki.ch.ic.ac.uk/wiki/images/7/72/EX1_OPTPRODUCTPM6.LOG file]
|-
|IRC
|[https://wiki.ch.ic.ac.uk/wiki/images/8/85/EX1_IRCPM6.LOG file]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_HEXADIENEOPTPM6%282%29.LOG file]
|-
|Dioxole
|[https://wiki.ch.ic.ac.uk/wiki/images/5/52/EX2_OPTDIOXOLEPM6.LOG file]
|-
|TS Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/a/a5/EX2_TSOPTPM6_EXO.LOG file]
|-
|TS Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/55/EX2_TSB3_EXO.LOG file]
|-
|Product Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_PRODUCT_B3_EXO.LOG file]
|-
|IRC Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9d/EX2_TSIRCPM6_EXO.LOG file]
|-
|TS Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4a/EX2_TSPM6_ENDO.LOG file]
|-
|TS Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/57/EX2_TSB3_ENDO.LOG file]
|-
|Product Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/0/03/EX2_PRODUCTOPT_ENDO.LOG file]
|-
|IRC Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e0/EX2_IRCPM6_ENDO.LOG file]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3d/EX3_XYLYLENE_OPT.LOG file]
|-
|SO<sub>2</sub>
|[https://wiki.ch.ic.ac.uk/wiki/images/9/97/EX3_SO2_REOPT.LOG file]
|-
|TS DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/EX3_TS_EXO.LOG file]
|-
|Product DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9f/EX3_PRODUCTOPTPM6_EXO.LOG file]
|-
|IRC DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/93/EX3_IRC_DA_EXO.LOG file]
|-
|TS DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/7/7a/EX3_TS_DA_ENDO.LOG file]
|-
|Product DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/8/87/EX3_PRODUCTOPT_ENDO.LOG file]
|-
|IRC DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f6/EX3_IRC_DA_ENDO.LOG file]
|-
|TS Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/3/37/EX3_CT_TS.LOG file]
|-
|Product Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4c/EX3_CT_PRODUCTOPT.LOG file]
|-
|IRC Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e6/EX3_CT_IRC.LOG file]
|}

File:EX2 PRODUCTOPT ENDO.LOG

2017-11-10T17:19:23Z

Sb6014: Sb6014 uploaded a new version of File:EX2 PRODUCTOPT ENDO.LOG

Thermochemdatasb6014

2017-11-10T17:18:40Z

Sb6014: /* eX 2 */

==eX 2==

{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3e/DIENE_OPTPM6_%282.2%29.LOG file]
|-
|Alkene
|[https://wiki.ch.ic.ac.uk/wiki/images/c/c8/ALKENE_OPTPM6_%282%29.LOG file]
|-
|TS
|[https://wiki.ch.ic.ac.uk/wiki/images/1/13/EX1_TSOPTPM6.LOG file]
|-
|Products
|[https://wiki.ch.ic.ac.uk/wiki/images/7/72/EX1_OPTPRODUCTPM6.LOG file]
|-
|IRC
|[https://wiki.ch.ic.ac.uk/wiki/images/8/85/EX1_IRCPM6.LOG file]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_HEXADIENEOPTPM6%282%29.LOG file]
|-
|Dioxole
|[https://wiki.ch.ic.ac.uk/wiki/images/5/52/EX2_OPTDIOXOLEPM6.LOG file]
|-
|TS Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/a/a5/EX2_TSOPTPM6_EXO.LOG file]
|-
|TS Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/55/EX2_TSB3_EXO.LOG file]
|-
|Product Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_PRODUCT_B3_EXO.LOG file]
|-
|IRC Exo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9d/EX2_TSIRCPM6_EXO.LOG file]
|-
|TS Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4a/EX2_TSPM6_ENDO.LOG file]
|-
|TS Endo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/5/57/EX2_TSB3_ENDO.LOG file]
|-
|Product Endo B3LYP
|[[EX2 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC Endo PM6
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e0/EX2_IRCPM6_ENDO.LOG file]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[https://wiki.ch.ic.ac.uk/wiki/images/3/3d/EX3_XYLYLENE_OPT.LOG file]
|-
|SO<sub>2</sub>
|[https://wiki.ch.ic.ac.uk/wiki/images/9/97/EX3_SO2_REOPT.LOG file]
|-
|TS DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/2/2e/EX3_TS_EXO.LOG file]
|-
|Product DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/9f/EX3_PRODUCTOPTPM6_EXO.LOG file]
|-
|IRC DA Exo
|[https://wiki.ch.ic.ac.uk/wiki/images/9/93/EX3_IRC_DA_EXO.LOG file]
|-
|TS DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/7/7a/EX3_TS_DA_ENDO.LOG file]
|-
|Product DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/8/87/EX3_PRODUCTOPT_ENDO.LOG file]
|-
|IRC DA Endo
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f6/EX3_IRC_DA_ENDO.LOG file]
|-
|TS Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/3/37/EX3_CT_TS.LOG file]
|-
|Product Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/4/4c/EX3_CT_PRODUCTOPT.LOG file]
|-
|IRC Cheletropic
|[https://wiki.ch.ic.ac.uk/wiki/images/e/e6/EX3_CT_IRC.LOG file]
|}

Thermochemdatasb6014

2017-11-10T17:06:52Z

Sb6014: /* eX 2 */

==eX 2==

{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[[DIENE OPTPM6 (2).LOG|file]]
|-
|Alkene
|[[ALKENE OPTPM6 (2).LOG|file]]
|-
|TS
|[[EX1 TSOPTPM6.LOG|file]]
|-
|Products
|[[EX1 OPTPRODUCTPM6.LOG|file]]
|-
|IRC
|[[file]]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[[EX2 HEXADIENEOPTPM6(2).LOG|file]]
|-
|Dioxole
|[[EX2 OPTDIOXOLEPM6.LOG|file]]
|-
|TS Exo PM6
|[[EX2 TSOPTPM6 EXO.LOG|file]]
|-
|TS Exo B3LYP
|[[EX2 TSB3 EXO.LOG|file]]
|-
|Product Exo B3LYP
|[https://wiki.ch.ic.ac.uk/wiki/images/f/f2/EX2_PRODUCT_B3_EXO.LOG file]
|-
|IRC Exo PM6
|[[EX2 TSIRCPM6 EXO.LOG|file]]
|-
|TS Endo PM6
|[[file]]
|-
|TS Endo B3LYP
|[[file]]
|-
|Product Endo B3LYP
|[[EX2 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC Endo PM6
|[[file]]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[[EX3 XYLYLENE OPT.LOG|file]]
|-
|SO<sub>2</sub>
|[[EX3 SO2 REOPT.LOG|file]]
|-
|TS DA Exo
|[[EX3 TS EXO.LOG |file]]
|-
|Product DA Exo
|[[EX3 PRODUCTOPTPM6 EXO.LOG |file]]
|-
|IRC DA Exo
|[[EX3 IRC DA ENDO.LOG|file]]
|-
|TS DA Endo
|[[EX3 TS DA ENDO.LOG|file]]
|-
|Product DA Endo
|[[EX3 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC DA Exo
|[[EX3 IRC DA EXO.LOG |file]]
|-
|TS Cheletropic
|[[EX3 CT TS.LOG|file]]
|-
|Product Cheletropic
|[[EX3 CT PRODUCTOPT.LOG|file]]
|-
|IRC Cheletropic
|[[EX3 CT IRC.LOG |file]]
|}

File:EX2 IRCB3 ENDO.LOG

2017-11-10T17:04:15Z

Sb6014:

Rep:Sb6014 TS 2017

2017-11-10T17:01:03Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement.

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

Method 2 was used to locate the transition state and determine the IRC for this reaction.

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermodynamic data ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

Method 3 was used to locate the transition state and determine the IRC for this reaction.

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

===Thermodynamic data ===

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== Conclusion ==

Computational methods were used to identify the transition state of various reactions. Thermodynamic data was also extracted, and the kinetic and thermodynamic data products were determined. The limitations of such methods was also discussed, and improvements to further investigations were also suggested.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

==Log files ==
{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[[DIENE OPTPM6 (2).LOG|file]]
|-
|Alkene
|[[ALKENE OPTPM6 (2).LOG|file]]
|-
|TS
|[[EX1 TSOPTPM6.LOG|file]]
|-
|Products
|[[EX1 OPTPRODUCTPM6.LOG|file]]
|-
|IRC
|[[file]]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[[EX2 HEXADIENEOPTPM6(2).LOG|file]]
|-
|Dioxole
|[[EX2 OPTDIOXOLEPM6.LOG|file]]
|-
|TS Exo PM6
|[[EX2 TSOPTPM6 EXO.LOG|file]]
|-
|TS Exo B3LYP
|[[EX2 TSB3 EXO.LOG|file]]
|-
|Product Exo B3LYP
|[[EX2 PRODUCT B3 EXO.LOG|file]]
|-
|IRC Exo PM6
|[[EX2 TSIRCPM6 EXO.LOG|file]]
|-
|TS Endo PM6
|[[file]]
|-
|TS Endo B3LYP
|[[file]]
|-
|Product Endo B3LYP
|[[EX2 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC Endo PM6
|[[file]]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[[EX3 XYLYLENE OPT.LOG|file]]
|-
|SO<sub>2</sub>
|[[EX3 SO2 REOPT.LOG|file]]
|-
|TS DA Exo
|[[EX3 TS EXO.LOG |file]]
|-
|Product DA Exo
|[[EX3 PRODUCTOPTPM6 EXO.LOG |file]]
|-
|IRC DA Exo
|[[EX3 IRC DA ENDO.LOG|file]]
|-
|TS DA Endo
|[[EX3 TS DA ENDO.LOG|file]]
|-
|Product DA Endo
|[[EX3 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC DA Exo
|[[EX3 IRC DA EXO.LOG |file]]
|-
|TS Cheletropic
|[[EX3 CT TS.LOG|file]]
|-
|Product Cheletropic
|[[EX3 CT PRODUCTOPT.LOG|file]]
|-
|IRC Cheletropic
|[[EX3 CT IRC.LOG |file]]
|}

Rep:Sb6014 TS 2017

2017-11-10T17:00:15Z

Sb6014: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement.

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

Method 2 was used to locate the transition state and determine the IRC for this reaction.

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermodynamic data ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

===Thermodynamic data ===

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== Conclusion ==

Computational methods were used to identify the transition state of various reactions. Thermodynamic data was also extracted, and the kinetic and thermodynamic data products were determined. The limitations of such methods was also discussed, and improvements to further investigations were also suggested.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

==Log files ==
{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[[DIENE OPTPM6 (2).LOG|file]]
|-
|Alkene
|[[ALKENE OPTPM6 (2).LOG|file]]
|-
|TS
|[[EX1 TSOPTPM6.LOG|file]]
|-
|Products
|[[EX1 OPTPRODUCTPM6.LOG|file]]
|-
|IRC
|[[file]]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[[EX2 HEXADIENEOPTPM6(2).LOG|file]]
|-
|Dioxole
|[[EX2 OPTDIOXOLEPM6.LOG|file]]
|-
|TS Exo PM6
|[[EX2 TSOPTPM6 EXO.LOG|file]]
|-
|TS Exo B3LYP
|[[EX2 TSB3 EXO.LOG|file]]
|-
|Product Exo B3LYP
|[[EX2 PRODUCT B3 EXO.LOG|file]]
|-
|IRC Exo PM6
|[[EX2 TSIRCPM6 EXO.LOG|file]]
|-
|TS Endo PM6
|[[file]]
|-
|TS Endo B3LYP
|[[file]]
|-
|Product Endo B3LYP
|[[EX2 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC Endo PM6
|[[file]]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[[EX3 XYLYLENE OPT.LOG|file]]
|-
|SO<sub>2</sub>
|[[EX3 SO2 REOPT.LOG|file]]
|-
|TS DA Exo
|[[EX3 TS EXO.LOG |file]]
|-
|Product DA Exo
|[[EX3 PRODUCTOPTPM6 EXO.LOG |file]]
|-
|IRC DA Exo
|[[EX3 IRC DA ENDO.LOG|file]]
|-
|TS DA Endo
|[[EX3 TS DA ENDO.LOG|file]]
|-
|Product DA Endo
|[[EX3 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC DA Exo
|[[EX3 IRC DA EXO.LOG |file]]
|-
|TS Cheletropic
|[[EX3 CT TS.LOG|file]]
|-
|Product Cheletropic
|[[EX3 CT PRODUCTOPT.LOG|file]]
|-
|IRC Cheletropic
|[[EX3 CT IRC.LOG |file]]
|}

Rep:Sb6014 TS 2017

2017-11-10T16:54:33Z

Sb6014:

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement.

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

===Thermodynamic data ===

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== Conclusion ==

Computational methods were used to identify the transition state of various reactions. Thermodynamic data was also extracted, and the kinetic and thermodynamic data products were determined. The limitations of such methods was also discussed, and improvements to further investigations were also suggested.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

==Log files ==
{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[[DIENE OPTPM6 (2).LOG|file]]
|-
|Alkene
|[[ALKENE OPTPM6 (2).LOG|file]]
|-
|TS
|[[EX1 TSOPTPM6.LOG|file]]
|-
|Products
|[[EX1 OPTPRODUCTPM6.LOG|file]]
|-
|IRC
|[[file]]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[[EX2 HEXADIENEOPTPM6(2).LOG|file]]
|-
|Dioxole
|[[EX2 OPTDIOXOLEPM6.LOG|file]]
|-
|TS Exo PM6
|[[EX2 TSOPTPM6 EXO.LOG|file]]
|-
|TS Exo B3LYP
|[[EX2 TSB3 EXO.LOG|file]]
|-
|Product Exo B3LYP
|[[EX2 PRODUCT B3 EXO.LOG|file]]
|-
|IRC Exo PM6
|[[EX2 TSIRCPM6 EXO.LOG|file]]
|-
|TS Endo PM6
|[[file]]
|-
|TS Endo B3LYP
|[[file]]
|-
|Product Endo B3LYP
|[[EX2 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC Endo PM6
|[[file]]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[[EX3 XYLYLENE OPT.LOG|file]]
|-
|SO<sub>2</sub>
|[[EX3 SO2 REOPT.LOG|file]]
|-
|TS DA Exo
|[[EX3 TS EXO.LOG |file]]
|-
|Product DA Exo
|[[EX3 PRODUCTOPTPM6 EXO.LOG |file]]
|-
|IRC DA Exo
|[[EX3 IRC DA ENDO.LOG|file]]
|-
|TS DA Endo
|[[EX3 TS DA ENDO.LOG|file]]
|-
|Product DA Endo
|[[EX3 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC DA Exo
|[[EX3 IRC DA EXO.LOG |file]]
|-
|TS Cheletropic
|[[EX3 CT TS.LOG|file]]
|-
|Product Cheletropic
|[[EX3 CT PRODUCTOPT.LOG|file]]
|-
|IRC Cheletropic
|[[EX3 CT IRC.LOG |file]]
|}

Rep:Sb6014 TS 2017

2017-11-10T16:51:57Z

Sb6014:

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

===Thermodynamic data ===

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== Conclusion ==

Computational methods were used to identify the transition state of various reactions. Thermodynamic data was also extracted, and the kinetic and thermodynamic data products were determined. The limitations of such methods was also discussed, and improvements to further investigations were also suggested.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

==Log files ==
{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[[DIENE OPTPM6 (2).LOG|file]]
|-
|Alkene
|[[ALKENE OPTPM6 (2).LOG|file]]
|-
|TS
|[[EX1 TSOPTPM6.LOG|file]]
|-
|Products
|[[EX1 OPTPRODUCTPM6.LOG|file]]
|-
|IRC
|[[file]]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[[EX2 HEXADIENEOPTPM6(2).LOG|file]]
|-
|Dioxole
|[[EX2 OPTDIOXOLEPM6.LOG|file]]
|-
|TS Exo PM6
|[[EX2 TSOPTPM6 EXO.LOG|file]]
|-
|TS Exo B3LYP
|[[EX2 TSB3 EXO.LOG|file]]
|-
|Product Exo B3LYP
|[[EX2 PRODUCT B3 EXO.LOG|file]]
|-
|IRC Exo PM6
|[[EX2 TSIRCPM6 EXO.LOG|file]]
|-
|TS Endo PM6
|[[file]]
|-
|TS Endo B3LYP
|[[file]]
|-
|Product Endo B3LYP
|[[EX2 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC Endo PM6
|[[file]]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[[EX3 XYLYLENE OPT.LOG|file]]
|-
|SO<sub>2</sub>
|[[EX3 SO2 REOPT.LOG|file]]
|-
|TS DA Exo
|[[EX3 TS EXO.LOG |file]]
|-
|Product DA Exo
|[[EX3 PRODUCTOPTPM6 EXO.LOG |file]]
|-
|IRC DA Exo
|[[EX3 IRC DA ENDO.LOG|file]]
|-
|TS DA Endo
|[[EX3 TS DA ENDO.LOG|file]]
|-
|Product DA Endo
|[[EX3 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC DA Exo
|[[EX3 IRC DA EXO.LOG |file]]
|-
|TS Cheletropic
|[[EX3 CT TS.LOG|file]]
|-
|Product Cheletropic
|[[EX3 CT PRODUCTOPT.LOG|file]]
|-
|IRC Cheletropic
|[[EX3 CT IRC.LOG |file]]
|}

Thermochemdatasb6014

2017-11-10T16:44:01Z

Sb6014: /* eX 2 */

==eX 2==

{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[[DIENE OPTPM6 (2).LOG|file]]
|-
|Alkene
|[[ALKENE OPTPM6 (2).LOG|file]]
|-
|TS
|[[EX1 TSOPTPM6.LOG|file]]
|-
|Products
|[[EX1 OPTPRODUCTPM6.LOG|file]]
|-
|IRC
|[[file]]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[[EX2 HEXADIENEOPTPM6(2).LOG|file]]
|-
|Dioxole
|[[EX2 OPTDIOXOLEPM6.LOG|file]]
|-
|TS Exo PM6
|[[EX2 TSOPTPM6 EXO.LOG|file]]
|-
|TS Exo B3LYP
|[[EX2 TSB3 EXO.LOG|file]]
|-
|Product Exo B3LYP
|[[EX2 PRODUCT B3 EXO.LOG|file]]
|-
|IRC Exo PM6
|[[EX2 TSIRCPM6 EXO.LOG|file]]
|-
|TS Endo PM6
|[[file]]
|-
|TS Endo B3LYP
|[[file]]
|-
|Product Endo B3LYP
|[[EX2 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC Endo PM6
|[[file]]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|[[EX3 XYLYLENE OPT.LOG|file]]
|-
|SO<sub>2</sub>
|[[EX3 SO2 REOPT.LOG|file]]
|-
|TS DA Exo
|[[EX3 TS EXO.LOG |file]]
|-
|Product DA Exo
|[[EX3 PRODUCTOPTPM6 EXO.LOG |file]]
|-
|IRC DA Exo
|[[EX3 IRC DA ENDO.LOG|file]]
|-
|TS DA Endo
|[[EX3 TS DA ENDO.LOG|file]]
|-
|Product DA Endo
|[[EX3 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC DA Exo
|[[EX3 IRC DA EXO.LOG |file]]
|-
|TS Cheletropic
|[[EX3 CT TS.LOG|file]]
|-
|Product Cheletropic
|[[EX3 CT PRODUCTOPT.LOG|file]]
|-
|IRC Cheletropic
|[[EX3 CT IRC.LOG |file]]
|}

File:EX2 PRODUCT B3 EXO.LOG

2017-11-10T16:43:44Z

Sb6014:

File:EX2 PRODUCTOPT ENDO.LOG

2017-11-10T16:43:08Z

Sb6014:

File:EX3 SO2 REOPT.LOG

2017-11-10T16:41:23Z

Sb6014:

File:EX3 XYLYLENE OPT.LOG

2017-11-10T16:40:35Z

Sb6014:

Thermochemdatasb6014

2017-11-10T16:39:32Z

Sb6014: /* eX 2 */

==eX 2==

{| class="wikitable"
!File
!Log File
|-
! colspan="2" |Exercise 1
|-
|Diene
|[[DIENE OPTPM6 (2).LOG|file]]
|-
|Alkene
|[[ALKENE OPTPM6 (2).LOG|file]]
|-
|TS
|[[EX1 TSOPTPM6.LOG|file]]
|-
|Products
|[[EX1 OPTPRODUCTPM6.LOG|file]]
|-
|IRC
|[[file]]
|-
! colspan="2" |Exercise 2
|-
|Cyclohexadiene
|[[EX2 HEXADIENEOPTPM6(2).LOG|file]]
|-
|Dioxole
|[[EX2 OPTDIOXOLEPM6.LOG|file]]
|-
|TS Exo PM6
|[[EX2 TSOPTPM6 EXO.LOG|file]]
|-
|TS Exo B3LYP
|[[EX2 TSB3 EXO.LOG|file]]
|-
|Product Exo PM6
|file
|-
|Product Exo B3LYP
|file
|-
|IRC Exo PM6
|[[EX2 TSIRCPM6 EXO.LOG|file]]
|-
|TS Endo PM6
|[[file]]
|-
|TS Endo B3LYP
|[[file]]
|-
|Product Endo PM6
|file
|-
|Product Endo B3LYP
|file
|-
|IRC Endo PM6
|[[file]]
|-
! colspan="2" |Exercise 3
|-
|o-Xylylene
|file
|-
|SO<sub>2</sub>
|file
|-
|TS DA Exo
|[[EX3 TS EXO.LOG |file]]
|-
|Product DA Exo
|[[EX3 PRODUCTOPTPM6 EXO.LOG |file]]
|-
|IRC DA Exo
|[[EX3 IRC DA ENDO.LOG|file]]
|-
|TS DA Endo
|[[EX3 TS DA ENDO.LOG|file]]
|-
|Product DA Endo
|[[EX3 PRODUCTOPT ENDO.LOG|file]]
|-
|IRC DA Exo
|[[EX3 IRC DA EXO.LOG |file]]
|-
|TS Cheletropic
|[[EX3 CT TS.LOG|file]]
|-
|Product Cheletropic
|[[EX3 CT PRODUCTOPT.LOG|file]]
|-
|IRC Cheletropic
|[[EX3 CT IRC.LOG |file]]
|}

Rep:Sb6014 TS 2017

2017-11-10T16:20:29Z

Sb6014: /* Thermodynamic data */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is a highly unfavourable product compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC (at PM6 as required), and confirmation that the structure has converged, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T16:18:15Z

Sb6014: /* Thermochemistry */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
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<size>300</size>
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</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
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<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
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<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
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<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure 23; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure x; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T16:17:31Z

Sb6014: /* MO diagram */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
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<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
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<size>300</size>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
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<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
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<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure 13 that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure x; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T16:15:47Z

Sb6014: /* Thermodynamic data */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure 31: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure x; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case (figure 26), where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T16:14:03Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
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|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
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| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
|
| Figure 28
| Figure 29
| Figure 30
|}

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T16:12:33Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
| Figure 25
| Figure 26
| Figure 27
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
| Figure 28
| Figure 29
| Figure 30
|Energy plot
|}

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T16:11:58Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
| Figure 25
| Figure 26
| Figure 27
|Energy plot
|-
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|-
| Figure 28
| Figure 29
| Figure 30
|Energy plot
|}

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T16:10:39Z

Sb6014: /* Thermodynamic data */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

In the IRCs shown in figures 25-27, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T16:08:23Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T16:06:27Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|400px ]]
|[[File:DA_ENDO_GIF.gif|400px]]
|[[File:CT_IRC_GIF.gif|400px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:52:18Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
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<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|300px ]]
|[[File:DA_ENDO_GIF.gif|300px]]
|[[File:CT_IRC_GIF.gif|300px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:51:38Z

Sb6014:

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
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<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
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|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:49:44Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|300px ]]
|[[File:DA_ENDO_GIF.gif|300px]]
|[[File:CT_IRC_GIF.gif|300px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:49:17Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|200px ]]
|[[File:DA_ENDO_GIF.gif|200px]]
|[[File:CT_IRC_GIF.gif|200px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:48:46Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
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<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
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<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
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<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|50px|frame|center | Figure 24: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

File:EX2 ENDO SECONDORB SB6014.png

2017-11-10T15:46:11Z

Sb6014: Sb6014 uploaded a new version of File:EX2 ENDO SECONDORB SB6014.png

Rep:Sb6014 TS 2017

2017-11-10T15:44:59Z

Sb6014: /* Thermochemistry */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure 23: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:44:05Z

Sb6014: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure 18: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO10</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO11</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>
|-
| Figure 19: MO9
| Figure 20: MO10
| Figure 21: MO11
| Figure 22: MO12
|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure x: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:41:53Z

Sb6014: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
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<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
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<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure 13: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""</script>
</jmolApplet></jmol>

! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO6</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO7</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO8</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|-
| Figure 14: MO5
| Figure 15: MO6
| Figure 16: MO7
| Figure 17: MO8
|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure x: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:38:34Z

Sb6014: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
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<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure 12: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

{| class="wikitable"
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The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure x: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:37:40Z

Sb6014: /* Molecular Orbital diagram */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital Diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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|-
|Figure 7: MO1
|Figure 8: MO2
|Figure 9: MO3
|Figure 10: MO4

|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
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<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
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<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure x: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO5</title>
<color>white</color>
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The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
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Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure x: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:35:53Z

Sb6014:

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure 3: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure 4: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure 5: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure 6: ALKENE LUMO]]
|-
|Figure 3: DIENE HOMO
|Figure 4: DIENE LUMO
|Figure 5: ALKENE HOMO
|Figure 6: ALKENE LUMO
|-
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=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure x: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

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The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

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|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure x: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:33:22Z

Sb6014: /* References */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure X: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure X: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure X: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure X: ALKENE LUMO]]
|-
|Figure X: DIENE HOMO
|Figure X: DIENE LUMO
|ALKENE HOMO
|Figure X: ALKENE LUMO
|-
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=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure x: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

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The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

{| class="wikitable"
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Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure x: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

(2) Suarez, D.; Sordo, T. L.; Sordo, J. A. (1995). "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls". J. Org. Chem. 60 (9): 2848–2852. doi:10.1021/jo00114a039.

Rep:Sb6014 TS 2017

2017-11-10T15:30:10Z

Sb6014: /* Thermodynamic data */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure X: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure X: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure X: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure X: ALKENE LUMO]]
|-
|Figure X: DIENE HOMO
|Figure X: DIENE LUMO
|ALKENE HOMO
|Figure X: ALKENE LUMO
|-
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=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure x: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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<title>MO8</title>
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<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure x: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the lone pair of the oxygen (not involved in the reaction) and the developing pi-bond of the o-Xylylene, as shown in exercise 2 in figure 23; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy, indicating this is the thermodynamic product. The exo product suffers less steric hindrance than it's endo counterpart; this is illustrated well in the IRC gif for the endo case, where the non-reacting S=O bond experiences repulsion from the rest of the molecule, and moves away from the rest of the molecule.

The cheletropic case has both the highest reaction energy and the reaction barrier, indicating that it is highly unfavourable compared to the products of the Diels-Alder reaction. A possible explanation for this result could be that the 5-membered ring experiences more strain than the 6-membered ring in the Diels-Alder case. However, experimental evidence (2) shows that the cheletropic product should be thermodynamically favoured, owing to the retention of both S=O bonds. The energy of the cheletropic product, as seen directly in the IRC, has also been recorded in brackets in Table 3; this supports the aforementioned trend, but weakly so. Despite reoptimisations of the cheletropic product obtained from the IRC, and confirmation that a minimum had be obtained, the energy remained higher than the products of the Diels-Alder reaction. A possible explanation for this error is that the IRC calculated reached a local minimum at the products, as opposed to the global minimum. This is a likely error, as the programme was set to 'Recorrect steps: Never'. In order to improve this calculation, this setting should be changed.

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

Rep:Sb6014 TS 2017

2017-11-10T15:12:50Z

Sb6014: /* Thermochemistry */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure X: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure X: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure X: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure X: ALKENE LUMO]]
|-
|Figure X: DIENE HOMO
|Figure X: DIENE LUMO
|ALKENE HOMO
|Figure X: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO1</title>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO2</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO3</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""</script>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO4</title>
<color>white</color>
<size>300</size>
<uploadedFileContents>EX1_TS_MOS.LOG</uploadedFileContents>
<script>frame 1.2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""</script>
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|}

=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
<jmolApplet>
<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
<color>white</color>
<size>400</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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</jmol>

Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure x: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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<color>white</color>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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<size>300</size>
<uploadedFileContents>EX2_IRCTSENERGY_EXO.LOG</uploadedFileContents>
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|}

The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO9</title>
<color>white</color>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
<title>MO12</title>
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<uploadedFileContents>EX2_MOSIRCTS_ENDO_2.LOG</uploadedFileContents>
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|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond, as shown in figure X; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[[File:EX2_ENDO_SECONDORB_SB6014.png|100px|frame|center | Figure x: Secondary orbital interactions in the Endo case]]

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the S=O bond (not involved in bond-formation) and the pi-bond of the o-Xylylene; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

Rep:Sb6014 TS 2017

2017-11-10T15:10:46Z

Sb6014: /* Thermochemistry */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure X: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure X: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure X: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure X: ALKENE LUMO]]
|-
|Figure X: DIENE HOMO
|Figure X: DIENE LUMO
|ALKENE HOMO
|Figure X: ALKENE LUMO
|-
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
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<title> Figure 11: Vibration corresponding to reactive path for the Diels-Alder reactive </title>
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<uploadedFileContents>EX1_TSOPTPM6.LOG</uploadedFileContents>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure x: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
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The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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|}

Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the S=O bond (not involved in bond-formation) and the pi-bond of the o-Xylylene; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

File:EX2 ENDO SECONDORB SB6014.png

2017-11-10T15:10:41Z

Sb6014:

Rep:Sb6014 TS 2017

2017-11-10T14:55:50Z

Sb6014: /* Exercise 3: Diels-Alder vs Cheletropic */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure X: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure X: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure X: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure X: ALKENE LUMO]]
|-
|Figure X: DIENE HOMO
|Figure X: DIENE LUMO
|ALKENE HOMO
|Figure X: ALKENE LUMO
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

<jmol>
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<script>frame 15; vibration 2;rotate x -20; </script>
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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure x: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

{| class="wikitable"
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The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

{| class="wikitable"
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Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction GIF
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|Energy plot
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

The IRCs above, we observe how the unstable o-Xylylene ring is converted to a aromatised benzene ring; the aromatic stability imparted by this transformation is the driving force for this reaction.

==Thermodynamic data ==

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

Table 3 shows that the activation energy is lowest in the endo case; considering Arrhenius' equation again, we may conclude that this is the kinetically-favoured product, formed under kinetic conditions (room temperature, non-equilibrating conditions). This result may be explained by considering the favourable orbital interactions in the TS between the S=O bond (not involved in bond-formation) and the pi-bond of the o-Xylylene; this stabilisation results in a lower energy endo transition state, and thus, the endo product is formed faster.

The table also shows that the exo product is the lowest in energy

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

Rep:Sb6014 TS 2017

2017-11-10T14:37:30Z

Sb6014: /* Thermochemistry */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure X: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure X: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure X: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure X: ALKENE LUMO]]
|-
|Figure X: DIENE HOMO
|Figure X: DIENE LUMO
|ALKENE HOMO
|Figure X: ALKENE LUMO
|-
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! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure x: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
! style="background: #0D4F8B; color: white;" | <jmol><jmolApplet>
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The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

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Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart (235.09 kJ/mol at 6-31G(d)) This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/6-31G(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level (3.60 kJ/mol at 6-31G(d)), indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction model
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|IRC
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.

Rep:Sb6014 TS 2017

2017-11-10T14:29:40Z

Sb6014: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

For a given molecule, each geometry of said molecule will have an associated potential energy. Since geometry changes in a continuous fashion, the potential energy is also expected to change smoothly. This is the origin of a potential energy surface (PES). Wale (ref) states that the PES represents the potential energy of a given system as a function of all the relevant atomic or molecular coordinates. In larger, more complicated molecules where we have several degrees of freedom, all but one or two reaction coordinates are assumed to be held constant or unaffected during the course of measurement, yielding an '''energy profile'''

Minima on the PES are stationary points and represent the positions of reactants and products of the system; they represent the lowest energy of the system, and hence, the system spends most of it's time in these locations. Small displacements from the minima always lead to an increase in energy of the system. When fluctuations are significant, we find the energy of the system can increase to a maximum. Also a stationary point, we find these positions correspond to transition states. The second derivative here is negative; as a consequence we find the frequency calculated at this geometry will appear negative or as an imaginary number, as the force constant used to calculate the frequency is negative. We can use this information to locate and characterise transition states in the following exercises.

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

The [4+2] cycloaddition of butadiene with ethene was investigated. Method 2 was used to locate the transition state and determine the IRC. A frequency calculation on the TS found one negative frequency, corresponding to the energy maxima and transition state. A further IRC confirmed this was the transition structure. Figure 1 shows the reaction scheme, with the concerted formation of two sigma bonds.

[[File:Bondlengths.jpg|600px|frame|center | Figure 1: Cycloaddition of ethylene with butadiene reaction scheme with atom labels]]

===Molecular Orbital diagram===

[[File: Ex_1_MO_diagram2.png| 500px |frame|center | Figure 2: MO diagram for the reaction of butadiene with ethene, with symmetric (S), antisymmetric (AS), HOMO and LUMO labels]]

For the molecular orbital (MO) diagram shown in figure 2, the energies of the fragment orbitals (FOs) of butadiene and ethene can be explained qualitatively by considering the number of nodes in the FO; the greater the number of nodes the greater the energy of the FO. Gaussian can also be used to confirm the energies of these FOs. Due to conjugation within butadiene, we expect the HOMO-LUMO gap to be smaller, as is illustrated. The gap in the reacting FOs results in a small splitting between the FOs and MOs. A greater contribution of each FO to the corresponding MO is expected when they are close in energy, as is illustrated.

The MO diagram shows that the FOs involved in a reaction must be of the same symmetry for a reaction to be allowed. The resulting MOs are also symmetric (S) or asymmetric (AS). Therefore a reaction is allowed when the MOs are a) of the same symmetry label b) of similar energies. The orbital overlap integral is zero for symmetric-antisymmetric interactions, due to the presence of equal amounts of constructive and destructive overlap. The orbital overlap integral is non-zero for symmetric-symmetric and antisymmetric-antisymmetric interactions.

{| class="wikitable"
|-
|[[File: HOMO_DIENE.png| 300px| Figure X: DIENE HOMO]]
|[[File: LUMO_DIENE.png| 300px| Figure X: DIENE LUMO]]
|[[File: HOMO_ALKENE.png| 300px| Figure X: ALKENE HOMO]]
|[[File: LUMO_ALKENE.png| 300px| Figure X: ALKENE LUMO]]
|-
|Figure X: DIENE HOMO
|Figure X: DIENE LUMO
|ALKENE HOMO
|Figure X: ALKENE LUMO
|-
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=== Bond Lengths ===

As the reaction progresses, two sigma bonds are formed, one double bond is formed, and two double bonds are broken. We can observe the change in bond lengths using Gaussian; the bond lengths are tabulated in Table 1 below. Please refer to figure 1 for atom labels.

The typical sp<sup>3</sup> C-C bond length is 1.54 A and sp<sup>2</sup> C=C bond length is 1.33 A. In the reactants, we find the single bond C2-C3 of butadiene is shorter than expected, due to the conjugation of the molecules. All other bonds are of expected length.

C6-C1 and C4-C5 correspond to the two new sigma bonds to be formed; as the bond lengths match the expected figure of 1.33A for a C-C bond, and we can conclude that these bonds are successfully formed. The corresponding double bonds C1-C2 and C3-C4 elongate from 1.33 A to 1.54 A signifying the change from a double to a single bond.

In the transition state, we expect bond lengths to be of intermediate value between the the Van der Waals diameter and products, showing that geometry is gradually changing towards the products. The Van der Waals radius of carbon is 1.70 A, which means the length of the new sigma bonds must be between 3.4 A and 1.54 A in the transition state; C6-C1 and C4-C5 both have bond lengths of 2.11 A in the transition state, indicating the reactants are close enough for a bond to form.

{| class="wikitable"
|+ Table 1: C-C Bond lengths (Angstroms)
|-
!
!Reactant
!Transition State
!Products
|-
!C1-C2
|1.335
|1.380
|1.541
|-
!C2-C3
|1.468
|1.411
|1.338
|-
!C3-C4
|1.335
|1.380
|1.541
|-
!C4-C5
|n/a
|2.115
|1.540
|-
!C5-C6
|1.327
|1.382
|1.541
|-
!C6-C1
|n/a
|2.115
|1.540
|}

===Vibration corresponding to reactive path at transition state===

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Figure 11 shows the vibration corresponding to the reactive path. The frequency shown here is the negative frequency calculated at energy maxima, as explained in the introduction. The stretch is symmetrical and the terminal carbons of both reactants move towards each other at the same time. Therefore, the formation of the two bonds is synchronous.

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

[[File:EX2_Reaction_Scheme.png|600px|frame|center | Figure x: Cycloaddition of cyclohexadiene with 1,3-Dioxole reaction scheme]]

=== MO diagram ===

[[File:EX_2_EXO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Exo transition state ]]

{| class="wikitable"
|-
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The MO diagram of the exo product was constructed using the relative energies found from Gaussian. Whilst these energies cannot be used as absolute values, they do indicate the relative placing of MOs in the diagram. We can see in figure X that the HOMO of the diene (cyclohexadiene) is lower than the HOMO of the dienophile (1,3 dioxole). This indicates an inverse demand DA reaction, where the greatest orbital interaction is found between the LUMO of the diene and HOMO of the dienophile. The high energy HOMO of the dienophile may be explained by considering the lone pair electrons in the two oxygen atoms of the ring; the electron donating groups raise the energy of the dienophile, thus its MOs lie higher in energy and we see an inverse demand in the reaction.

[[File:EX_2_ENDO_MO_DIAGRAM.png|100px|frame|center | Figure x: MO diagram for the Endo transition state ]]

{| class="wikitable"
|-
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Like the Exo case, the endo case also shows an inverse demand reaction.

=== Thermochemistry ===

{| class="wikitable"
|+ Table 2: Thermodynamic data from reaction 2 at two optimisation levels
!
! colspan="2" |Sum of electronic and thermal Free Energies (kJ/mol)
|-
!
!PM6
!B3LYP/6-31G(d)
|-
!Cyclohexadiene
|306.855336
|<nowiki>-612593.193227</nowiki>
|-
!1,3-Dioxole
|<nowiki>-137.258525</nowiki>
|<nowiki>-701187.43398</nowiki>
|-
!Exo TS
|364.689854
|<nowiki>-1313614.286016</nowiki>
|-
!Exo product
|99.7099673
|<nowiki>-1313845.77899</nowiki>
|-
!Exo reaction barrier
|195.093043
|166.341191
|-
!Exo reaction energy
|<nowiki>-69.8868437</nowiki>
|<nowiki>-65.151783</nowiki>
|-
!Endo TS
|362.166749
|<nowiki>-1313849.37856</nowiki>
|-
!Endo product
|99.26482492
|<nowiki>-1313849.3733</nowiki>
|-
!Endo reaction barrier
|192.569938
|158.480447
|-
!Endo reaction energy
|<nowiki>-70.33198608</nowiki>
|<nowiki>-68.746093</nowiki>
|}

At the PM6 optimisation level, the endo reaction barrier is 2.52 kJ/mol lower than it's exo counterpart. This is expected, as we expect secondary orbital interactions between the p-orbitals of the oxygens in the dioxole with the pi-orbitals of the developing pi-bond; this lowers the energy of the transition state, lowering the reaction barrier (activation energy - Ea). Using Arrhenius' relationship between rate and activation energy, we can conclude that the endo product is formed fastest, and kinetically favoured. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

The endo product is also 0.45 kJ/mol lower than its exo counterpart at the PM6 optimisation level, indicating the endothermic product is also the most thermodynamically stable. This may be explained by considering the steric hindrance observed both in the exo TS and product. In the exo TS, where the hydrogens are on an opposite face to the carbon bridge, we will observe steric hindrance with the rest of the dioxole ring, increasing the energy of the TS, the activation barrier and thus, decreasing the rate. Similarly, the hindrance is observed in the products, increasing its energy compared to the endo counterpart. A similar argument may be made using data from the B3LYP/G-31(d) optimisation.

[INSERT JMOL MOS OF HOMO ENDO TS, EXO TS +ORB INTERACTIONS]

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

[[File:Ex3_reactionscheme.png|100px|frame|center | Figure x: MO diagram for the reaction of O-Xylylene and SO2]]

{| class="wikitable"
!
!Exo *Note IRC is reversed
!Endo
!Cheletropic
|-
|Reaction model
|[[File:DA_EXO_GIF.gif|500px ]]
|[[File:DA_ENDO_GIF.gif|500px]]
|[[File:CT_IRC_GIF.gif|500px]]
|-
|IRC
|[[File:Ex3_da_exo.png]]
|[[File:Ex3_da_endo.png]]
|[[File:Ex3_CT.png]]
|}

{| class="wikitable"
|+ Table 3: Thermodynamic data from reaction 3, found at the PM6 optimisation level
!
!DA Exo
!DA Endo
!Cheletropic
|-
!O-Xylylene
| colspan="3" |467.564829
|-
!SO<sub>2</sub>
| colspan="3" |-313.138158
|-
!TS
|241.7481819154
|237.765298112
|260.5833639
|-
!Product
|56.3274812908
|56.96547784
|166.278178666 (52.38765569)
|-
!Reaction barrier
|87.32151092
|83.33862711
|106.1566929
|-
!Reaction energy
|<nowiki>-98.0991897</nowiki>
|<nowiki>-97.4611932</nowiki>
|11.85151 (-102.039)
|}

[[File:EX3_SB6014_PROFILE.png|500px|frame|center | Figure x: Reaction profile for the reaction of O-Xylylene and SO2]]

== References ==

(1) Wales, D. In Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge Molecular Science; Cambridge University Press: Cambridge, 2004; pp 1–118.