ChemWiki - User contributions [en]

Rep:Mod:CNLXXX

2017-02-10T07:07:43Z

Cn1314: /* Optimisation and Visualisation */

= Y3C Transition States and Reactivity =

== Introduction ==

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of its geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too due to force being the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product, because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product, as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some effect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. a and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO was gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mixing to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The table below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the .log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and those on the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01.
The endo-product was calculated to be the thermodynamically more stable product too, as seen by the more negative free energy difference. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. <ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref> The exo transition state doesn't benefit from this secondary orbital overlap.

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, and optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction, from reactants at infinite separation, to the final products. It can be seen that along the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC gif movie
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is certainly the thermodynamic one, however a higher relative temperature would be required to access it. The most favourable product is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions, but also to obtain thermodynamic data, hence allowing predictions to be made on the most likely products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms of dioxole. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T07:03:20Z

Cn1314: /* Introduction */

= Y3C Transition States and Reactivity =

== Introduction ==

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of its geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too due to force being the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product, because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product, as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some effect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. a and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO was gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mixing to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The table below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the .log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and those on the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01.
The endo-product was calculated to be the thermodynamically more stable product too, as seen by the more negative free energy difference. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. <ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref> The exo transition state doesn't benefit from this secondary orbital overlap.

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, and optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction, from reactants at infinite separation, to the final products. It can be seen that along the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is certainly the thermodynamic one, however a higher relative temperature would be required to access it. The most favourable product is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions, but also to obtain thermodynamic data, hence allowing predictions to be made on the most likely products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms of dioxole. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T07:00:00Z

Cn1314: /* Conclusion */

= Y3C Transition States and Reactivity =

== Introduction ==

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product, because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product, as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some effect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. a and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO was gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mixing to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The table below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the .log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and those on the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01.
The endo-product was calculated to be the thermodynamically more stable product too, as seen by the more negative free energy difference. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. <ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref> The exo transition state doesn't benefit from this secondary orbital overlap.

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, and optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction, from reactants at infinite separation, to the final products. It can be seen that along the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is certainly the thermodynamic one, however a higher relative temperature would be required to access it. The most favourable product is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions, but also to obtain thermodynamic data, hence allowing predictions to be made on the most likely products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms of dioxole. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:57:27Z

Cn1314: /* Energies of the Reactions */

= Y3C Transition States and Reactivity =

== Introduction ==

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product, because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product, as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some effect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. a and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO was gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mixing to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The table below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the .log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and those on the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01.
The endo-product was calculated to be the thermodynamically more stable product too, as seen by the more negative free energy difference. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. <ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref> The exo transition state doesn't benefit from this secondary orbital overlap.

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, and optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction, from reactants at infinite separation, to the final products. It can be seen that along the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is certainly the thermodynamic one, however a higher relative temperature would be required to access it. The most favourable product is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:56:07Z

Cn1314: /* Optimisation and Visualisation */

= Y3C Transition States and Reactivity =

== Introduction ==

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product, because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product, as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some effect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. a and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO was gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mixing to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The table below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the .log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and those on the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01.
The endo-product was calculated to be the thermodynamically more stable product too, as seen by the more negative free energy difference. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. <ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref> The exo transition state doesn't benefit from this secondary orbital overlap.

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, and optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction, from reactants at infinite separation, to the final products. It can be seen that along the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:53:05Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

= Y3C Transition States and Reactivity =

== Introduction ==

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product, because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product, as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some effect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. a and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO was gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mixing to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The table below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the .log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and those on the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01.
The endo-product was calculated to be the thermodynamically more stable product too, as seen by the more negative free energy difference. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. <ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref> The exo transition state doesn't benefit from this secondary orbital overlap.

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:12:57Z

Cn1314: /* Introduction */

= Y3C Transition States and Reactivity =

== Introduction ==

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:10:34Z

Cn1314: /* Energies in Reactions */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:10:01Z

Cn1314: /* Exercise 1 - Reaction of Butadiene with Ethene */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:09:07Z

Cn1314: /* Energies in Reactions */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>
|}

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:05:50Z

Cn1314: /* Exercise 1 - Reaction of Butadiene with Ethene */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>
|}

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:04:09Z

Cn1314: /* Energies in Reactions */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>340</size>
<script>frame 7;vibration 2; rotate y 15</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T06:01:18Z

Cn1314: /* Vibrational Visualisation */

Rep:Mod:CNLXXX

2017-02-10T05:55:41Z

Cn1314: /* Vibrational Visualisation */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 11;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 10;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 9;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 8;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 7;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 6;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 5;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 4;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T05:52:34Z

Cn1314: /* Vibrational Visualisation */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 18;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 17;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 16;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 15;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 14;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 13;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 12;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 11;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 10;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T05:49:58Z

Cn1314: /* Vibrational Visualisation */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 20;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 21;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 22;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 23;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 24;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T05:44:07Z

Cn1314: /* Exercise 1 - Reaction of Butadiene with Ethylene */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

==Exercise 1 - Reaction of Butadiene with Ethene==

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T05:35:40Z

Cn1314: /* Conclusion */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

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

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

==References==

Rep:Mod:CNLXXX

2017-02-10T05:35:05Z

Cn1314: /* Conclusion */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

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

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions and also to obtain thermodynamic data, hence allowing predictions to be made on the major products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.

Rep:Mod:CNLXXX

2017-02-10T05:16:51Z

Cn1314: /* Introduction */

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of it's geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES.
At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too as force is the negative of the first derivative.
The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and the optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

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

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Rep:Mod:CNLXXX

2017-02-10T04:17:58Z

Cn1314:

= Y3C Transition States and Reactivity =

== Introduction ==
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>260</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

===Bond Length Measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

===Vibrational Visualisation===

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

===MO Diagrams===

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

===MO Calculations and Jmols===

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Energies in Reactions===

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

===Optimisation and Visualisation===

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

===Energies of the Reactions===

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

==Conclusion==

Rep:Mod:CNLXXX

2017-02-10T04:05:26Z

Cn1314: /* Exercise 1 - Reaction of Butadiene with Ethylene */

= Y3C Transition States and Reactivity =

= Introduction =
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

=Exercise 1 - Reaction of Butadiene with Ethylene=

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

==Bond Length Measurements==
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

==Vibrational Visualisation==

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

==MO Diagrams==

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

==MO Calculations and Jmols==

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

==Energies in Reactions==

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic Reaction=

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

==Optimisation and Visualisation==

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

==Energies of the Reactions==

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

=Conclusion=

Rep:Mod:CNLXXX

2017-02-10T04:04:45Z

Cn1314: /* MO Calculations and Jmols */

= Y3C Transition States and Reactivity =

= Introduction =
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

! align="center"| <math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

==Bond Length Measurements==
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

==Vibrational Visualisation==

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

==MO Diagrams==

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

==MO Calculations and Jmols==

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | TS
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>260</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

==Energies in Reactions==

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic Reaction=

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

==Optimisation and Visualisation==

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

==Energies of the Reactions==

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

=Conclusion=

Rep:Mod:CNLXXX

2017-02-10T04:00:41Z

Cn1314: /* Exercise 1 - Reaction of Butadiene with Ethylene */

= Y3C Transition States and Reactivity =

= Introduction =
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Reaction1.jpeg|center|500x500px]] '''Cycloaddition of ethene and butadiene'''
|}

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercise1_MO_2.jpeg_copy....jpeg|center|500x500px]] '''MO diagram for formation of TS'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO's
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

! align="center"| <math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

==Bond Length Measurements==
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref> , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

==Vibrational Visualisation==

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

==MO Diagrams==

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

==MO Calculations and Jmols==

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

==Energies in Reactions==

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic Reaction=

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

==Optimisation and Visualisation==

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

==Energies of the Reactions==

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

=Conclusion=

File:Cn1314 Reaction1.jpeg

2017-02-10T03:39:17Z

Cn1314:

File:Cn1314 Exercise1 MO 2.jpeg copy....jpeg

2017-02-10T03:38:42Z

Cn1314:

Rep:Mod:CNLXXX

2017-02-10T03:18:35Z

Cn1314: /* Y3C Transition States and Reactivity */

= Y3C Transition States and Reactivity =

= Introduction =
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

==MO Diagrams==

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

==MO Calculations and Jmols==

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

==Energies in Reactions==

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic Reaction=

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

==Optimisation and Visualisation==

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

==Energies of the Reactions==

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

=Conclusion=

Rep:Mod:CNLXXX

2017-02-10T03:15:01Z

Cn1314: /* Exercise 3 - Diels-Alder vs Cheletropic */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

==MO Diagrams==

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

==MO Calculations and Jmols==

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

==Energies in Reactions==

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic Reaction=

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

==Optimisation and Visualisation==

The TS's were calculated by starting with the product and working backwards, optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction to from reactants at infinite separation, to the final products. It can be seen that during the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

==Energies of the Reactions==

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. The most favourable product is likely to is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

=Conclusion=

Rep:Mod:CNLXXX

2017-02-10T02:49:59Z

Cn1314: /* Energies of the Reactions */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

==MO Diagrams==

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

==MO Calculations and Jmols==

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

==Energies in Reactions==

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

==Energies of the Reactions==

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. Below is a reaction profile which illustrates this more clearly.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|650x650px]] '''Reaction 3 Energy Profile'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-10T02:44:03Z

Cn1314: /* Exercise 3 - Diels-Alder vs Cheletropic */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

==MO Diagrams==

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

==MO Calculations and Jmols==

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

==Energies in Reactions==

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 3 Scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

==Energies of the Reactions==

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is significantly the thermodynamic one, however a higher temperature would be required to access it. Below is a reaction profile which illustrates this more clearly.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Rection_coordinate_part3_2.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

File:Cn1314 Rection coordinate part3 2.jpeg

2017-02-10T02:43:36Z

Cn1314:

File:Cn1314 Rection coordinate part3.jpeg

2017-02-10T02:38:38Z

Cn1314:

Rep:Mod:CNLXXX

2017-02-10T02:12:05Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

==MO Diagrams==

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO could be gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mining to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

==MO Calculations and Jmols==

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

==Energies in Reactions==

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-10T02:00:12Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

==MO Diagram==

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

==MO Calculations and Jmols==

The diagram below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

==Energies in Reactions==

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction Scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-10T01:50:41Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-10T01:40:05Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" |
! colspan="2" style="text-align: center;" |
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
</jmol></jmolApplet>
<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-10T01:33:53Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.<ref>1 C. F. Tormena, V. Lacerda Jr and K. T. d. Oliveira, Journal of the Brazilian Chemical Society, 2010, 21, 112-118.</ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
</jmol></jmolApplet>

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-10T01:27:02Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Rection coordinate part2.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

As can be seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the lower product energy. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. <ref> Tormena, Claudio F., Valdemar Lacerda Jr, and Kleber T. de Oliveira. "Revisiting the Stability of endo/exo Diels-Alder Adducts between Cyclopentadiene and 1, 4-benzoquinone." Journal of the Brazilian Chemical Society 21.1 (2010): 112-118.
APA </ref>

<jmol><jmolApplet>
<title>HOMO showing secondary orbital interaction in endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

File:Cn1314 Rection coordinate part2.jpeg

2017-02-10T01:26:08Z

Cn1314:

Rep:Mod:CNLXXX

2017-02-09T23:56:30Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS despite the exo-product being the more thermodynamically favourable product. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01.

<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-09T23:54:13Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS despite the exo-product being the more thermodynamically favourable product. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01.

{| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo cutoff 0.01; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-09T23:31:26Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo product is ..... ==look up==

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

===Are there secondary orbital interactions?===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-09T23:29:55Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
|
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
|
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo product is ..... ==look up==

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

===Are there secondary orbital interactions?===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-09T23:26:37Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
|-
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo product is ..... ==look up==

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

===Are there secondary orbital interactions?===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-09T23:25:27Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
|-
|
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo product is ..... ==look up==

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

===Are there secondary orbital interactions?===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-09T23:21:30Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | MO Diagram
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
|
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo product is ..... ==look up==

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

===Are there secondary orbital interactions?===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-09T23:16:42Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="1" style="text-align: center;" | Transition State
! colspan="2" style="text-align: center;" | MO Diagram
|-
| style="text-align: center;" | Endo
| style="text-align: center;" | Exo
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
|-
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo product is ..... ==look up==

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

===Are there secondary orbital interactions?===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

Rep:Mod:CNLXXX

2017-02-09T22:54:31Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Endo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 exo.jpeg|center|500x500px]] '''Exo Transition State'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo product is ..... ==look up==

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

===Are there secondary orbital interactions?===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}

File:Cn1314 Exercise2 exo.jpeg

2017-02-09T22:53:10Z

Cn1314:

Rep:Mod:CNLXXX

2017-02-09T22:38:11Z

Cn1314: /* Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole */

== Y3C Transition States and Reactivity ==
=== Introduction ===
(Briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?))

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

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_reaction_scheme.jpg|center|500x500px]] '''The reaction scheme'''
|}

Please see the MO diagram of the reaction below (drawn in ChemDraw):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 MO 2.jpeg|center|500x500px]] '''The reaction scheme'''
|}

Below is a table which includes JMol objects showing the MO's involved in the reactants and transition state of the reaction. The HOMO and LUMO of both ethene and butadiene are shown, as well as the four MO's they produce.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
!Ethylene MOs
!Butadiene MOs
! colspan="2" |Transition state MO
|-
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|-
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_ETHENE_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_BUTADIENE_0_DIHEDRAL_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>300</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG </uploadedFileContents>
</jmolApplet></jmol>
|}

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are of ungerade (u) symmetry, and the LUMO of butadiene inteacts with the HOMO of ethene as both are gerade (g) symmetry. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

<math>S_{AB}= \int{\psi}_ A^* {\psi}_ B dV</math>

where <math>\int{\psi}_ A^*</math> is the wavefunction of atom A and <math>{\psi}_ B</math> is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. antisymmetric (AS) and AS, or symmetric (S) and S. If the wavefunctions are of opposite symmetry then the integral is equal to zero and there will be no mixing.

===Bond length measurements===
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314_mechanism.jpg|center|500x500px]] '''[4+2] cycloaddition of butadiene and ethene '''
|}

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively. <ref> 1 F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, J. Chem. Soc. Perkin Trans. '''12''', 1987, S1-S19.</ref> <ref> J. Clayden, N. Greeves and S. Warren, ''Organic Chemistry'', Oxford University Press, New York, 2nd edn., 2001.</ref>

=== measure bond lengths in Gaussian===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" | Bond
! colspan="3" style="text-align: center; width: 200px;" | Bond Length (Å)
|-
| style="text-align: center; width: 100px;" | Reactants
| style="text-align: center; width: 100px;" | Transition State
| style="text-align: center; width: 100px;" | Product
|-
| style="text-align: center;" |C1-C2
| style="text-align: center;" | 1.32731
| style="text-align: center;" | 1.38177
| style="text-align: center;" | 1.54076
|-
| style="text-align: center;" |C2-C3
| style="text-align: center;" | -
| style="text-align: center;" | 2.11512
| style="text-align: center;" | 1.54003
|-
| style="text-align: center;" |C3-C4
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37974
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C4-C5
| style="text-align: center;" | 1.46835
| style="text-align: center;" | 1.41110
| style="text-align: center;" | 1.33736
|-
| style="text-align: center;" |C5-C6
| style="text-align: center;" | 1.33530
| style="text-align: center;" | 1.37982
| style="text-align: center;" | 1.50034
|-
| style="text-align: center;" |C6-C1
| style="text-align: center;" | -
| style="text-align: center;" | 2.11437
| style="text-align: center;" | 1.54004
|}

As can be seen from the table above, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds.
From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length.
The final 6 bond lengths in the product compare very well to typical bond lengths listed above.
The Van der Waal radius of a typical C atom is 1.70 Å <ref> S. S. Batsanov, Inorg. Mater., 2001, '''37''', 871–885.</ref>. Since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) are 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage of the reaction.

The vibration below corresponds to the vibration of the reaction path. It can be concluded that the formation of the two bonds in synchronous i.e. at the same time as each other.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
|<jmol><jmolApplet>
<title>Vibration corresponding to reaction path at TS</title>
<color>white</color>
<size>300</size>
<script>frame 19;vibration 2 </script>
<uploadedFileContents>Cn1314_TS_ZERO_OPT_2.LOG</uploadedFileContents>

</jmolApplet></jmol>
|}

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

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product.. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some affect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other. The exo product is likely to be the most stable due to steric reasons.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 scheme.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

The MO diagrams below shows the orbitals which interact to form both TS's respectively. A and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is likely to be different. We discuss the relative energies of the two TS's later.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:Cn1314 Exercise2 endo.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center;" | Transition State
! colspan="4" style="text-align: center;" | Molecular Orbital
|-
| style="text-align: center;" | HOMO -1
| style="text-align: center;" | HOMO
| style="text-align: center;" | LUMO
| style="text-align: center;" | LUMO +1
|-
|Exo
| <jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 20; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_EXO_B3LYP_TS.LOG</uploadedFileContents>
</jmolApplet></jmol>
|-
|Endo
|<jmol><jmolApplet>
<title>HOMO -1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 40; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 41; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 42; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
| <jmol><jmolApplet>
<title>LUMO +1</title>
<color>white</color>
<size>300</size>
<script>frame 46; mo 43; mo dots mesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>cn1314_TS_ENDO_B3LYP_TS_33.LOG</uploadedFileContents>
</jmolApplet></jmol>
|}

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the log output file in the "thermochemistry" section of the reactants, transition states and products.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="2" style="text-align: center; width: 250px;" | Energies (kJ/mol)
|-
| style="text-align: center;" | Exo TS
| style="text-align: center;" | Endo TS
|-
|style="text-align: center;" |'''E<sub>a</sub>'''
| style="text-align: center;"|166.3029563
| style="text-align: center;"|158.4660316
|-
|style="text-align: center;" |'''ΔG'''
| style="text-align: center;"|-65.0013542
| style="text-align: center;"|-71.9882576
|}

As can be seen in the table and diagram below, the endo product is ..... ==look up==

===Obtain IRC's so that Change in Free energy can be calculated - then reaction profile can be drawn.===

===Are there secondary orbital interactions?===

=Exercise 3 - Diels-Alder vs Cheletropic=

The cycloaddition of o-Xylylene to SO2 can go wither via a Diels-Alder reaction or a cheletropic one. In the part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! align="center"| [[File:cn1314_Exercie_3.jpeg|center|500x500px]] '''Reaction 2 scheme'''
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|-
! Reaction pathway
! IRC
! IRC Graph
|-
|Cheletropic
| align="center"| [[File:Cn1314 Cheletropic.gif|center|500x500px]]
| align="center"| [[File:Cn1314 CHELETROPIC.png|center|500x500px]]
|-
|Endo Diels-Alder
| align="center"| [[File:Cn1314 Endo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Endo IRC pathway.png|center|500x500px]]
|-
|Exo Diels-Alder
| align="center"| [[File:Cn1314 Exo.gif|center|500x500px]]
| align="center"| [[File:Cn1314 Exo IRC pathway.png|center|500x500px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! rowspan="2" style="text-align: center; width: 100px;" |
! colspan="3" style="text-align: center; width: 250px;" | Energy (kJ/mol)
|-
| style="text-align: center;" | Exo
| style="text-align: center;" | Endo
| style="text-align: center;" | Cheletropic
|-
| style="text-align: center;" |'''Activation Energy (E<sub>a</sub>)'''
| style="text-align: center;"|241.7422179
| style="text-align: center;"|236.4782199
| style="text-align: center;"|260.0808844
|-
| style="text-align: center;" |'''Free Energy Change of reaction (ΔG)'''
| style="text-align: center;"|-172.1908103
| style="text-align: center;"|-168.4238356
| style="text-align: center;"|-231.4465991
|}