ChemWiki - User contributions [en]

Rep:Mod:AO1995

2015-12-04T16:21:42Z

Ao2013: /* Comparsion between endo and exo */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does fullytake into account the electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride ====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 using the TS berney method. The log file of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-
|C17-C18 ||1.41012
|-
|C6-C5 ||1.39440
|-
|C5-C4 ||1.39677
|-
|C4-C1 ||1.39437
|-
|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-
|C17-C18 ||1.40850
|-
|C3-C3 ||1.39308
|-
|C5-C4 ||1.39722
|-
|C5-C6 ||1.39304
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).

The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction[5].The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce favorable reaction pathways and activation energies.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.

Rep:Mod:AO1995

2015-12-04T12:55:58Z

Ao2013: /* Comparsion between endo and exo */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does fullytake into account the electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride ====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 using the TS berney method. The log file of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-
|C17-C18 ||1.41012
|-
|C6-C5 ||1.39440
|-
|C5-C4 ||1.39677
|-
|C4-C1 ||1.39437
|-
|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-
|C17-C18 ||1.40850
|-
|C3-C3 ||1.39308
|-
|C5-C4 ||1.39722
|-
|C5-C6 ||1.39304
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
In both cases, the appea
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction[5].The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce favorable reaction pathways and activation energies.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.

Rep:Mod:AO1995

2015-12-04T12:49:27Z

Ao2013: /* Comparsion between endo and exo */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does fullytake into account the electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride ====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 using the TS berney method. The log file of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-
|C17-C18 ||1.41012
|-
|C6-C5 ||1.39440
|-
|C5-C4 ||1.39677
|-
|C4-C1 ||1.39437
|-
|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction[5].The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce favorable reaction pathways and activation energies.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.

Rep:Mod:AO1995

2015-12-04T12:27:48Z

Ao2013: /* Regioselectivity of Diels alder reactions */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does fullytake into account the electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride ====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 using the TS berney method. The log file of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction[5].The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce favorable reaction pathways and activation energies.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.

Rep:Mod:AO1995

2015-12-04T12:15:30Z

Ao2013: /* Endo Transition State Optimisation */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does fullytake into account the electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 using the TS berney method. The log file of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction[5].The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce favorable reaction pathways and activation energies.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.

Rep:Mod:AO1995

2015-12-04T12:07:35Z

Ao2013: /* Results Table */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does fullytake into account the electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction[5].The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce favorable reaction pathways and activation energies.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.

Rep:Mod:AO1995

2015-12-04T12:03:16Z

Ao2013: /* Conclusion */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does not account for electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction[5].The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce favorable reaction pathways and activation energies.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.

Rep:Mod:AO1995

2015-12-04T12:02:17Z

Ao2013: /* References */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does not account for electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction[5].The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce the reaction pathways.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.

Rep:Mod:AO1995

2015-12-04T11:53:50Z

Ao2013: /* Comparsion between endo and exo */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does not account for electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction[5].The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce the reaction pathways.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.doi:http://pubs.acs.org/doi/abs/10.1021/jo00384a016

Rep:Mod:AO1995

2015-12-04T11:53:10Z

Ao2013: /* References */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does not account for electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction.The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .
====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce the reaction pathways.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

5.Fox, M., Cardona, R. and Kiwiet, N. (1987). Steric effects vs. secondary orbital overlap in Diels-Alder reactions. MNDO and AM1 studies. The Journal of Organic Chemistry, 52(8), pp.1469-1473.doi:http://pubs.acs.org/doi/abs/10.1021/jo00384a016

Rep:Mod:AO1995

2015-12-04T11:51:09Z

Ao2013: /* Results Table */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does not account for electron-electron interactions hence the energies tend to be higher which is consistent with the data. DFT on the other hand includes these Coulombic interactions.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction.The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .
====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce the reaction pathways.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

Rep:Mod:AO1995

2015-12-04T11:41:19Z

Ao2013: /* Results Table */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

The point group for both basis sets used did not change indicating that both basis sets used describes the geometry reasonably well.It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. As a result ,using HF will provide reasonable results for geometry. however, In order to obtain an accurate value for the energy, A higher level of theory must be used i.e DFT. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

The large discrepancy in energy between the HF and DFT method arises from the difference in the how the methods work. HF desribes the system by solving many electron wave functions using slaters determinant. This does not account for electron-electron interactions hence the energies tend to be higher which is consistent with the data.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction.The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .
====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce the reaction pathways.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

Rep:Mod:AO1995

2015-12-04T11:12:08Z

Ao2013: /* Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC) */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction.The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .
====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce the reaction pathways.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

Rep:Mod:AO1995

2015-12-04T11:11:25Z

Ao2013: /* Conclusion */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction.The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .
====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce the reaction pathways.

====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

Rep:Mod:AO1995

2015-12-04T11:10:28Z

Ao2013:

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of potential energy surface is equal to 0 and the second derivative is less than 0.
These structures cannot be experimentally determined but can be modeled using computational methods. There are various approaches and levels of theory that can be used. Modelling a system is a comprise between the level of accuracy and how computationally expensive it is. Three different reaction were investigate:the Cope Rearrangement of 1,5-hexadiene and Diels alder reactions. Three different level of theory were used. AM1 semi empirical which was the least accurate method as the atomic orbital basis set is not specified. HF which is computationally more expensive as it requires solving many electron wave function via slater determinants. The most accurate method used was DFT which uses functionals of the electron density to obtain the optimised structure.

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement which is concerted[1].This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature. The activation energies were determined by look at the thermochemistry data which is shown in the first table. The second table shows the conversion to kcal/mol. The activation energy is calculated by finding the energy difference between the reactants and the transition state energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder cycloaddtion==
====Background ====
Diels-Alder cyclo additions are a class of pericyclic reactions where two sigma bonds are formed and one pi bond is broken.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54[2] and 1.46[3] Å respectively while the Van der waals radius is 1.7 Å[4]. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction.The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .
====Conclusion====

In conclusion, the use of computational methods can be used to predict the transition structure and provide greater insight as to how the reaction proceeds by analysis the MOs. Various transition structures of different reactions were examined as a result it was possible to deduce the reaction pathways.

To
====References====
1. Cope, A.C., Hardy, E.M.. (1940). The Introduction of Substituted Vinyl Groups. V. A Rearrangement Involving the Migration of an Allyl Group in a Three-Carbon System. J. Am. Chem. Soc. 62 (2), 441-444.

2.Pauling, L. (1931). THE NATURE OF THE CHEMICAL BOND. II. THE ONE-ELECTRON BOND AND THE THREE-ELECTRON BOND. J. Am. Chem. Soc., 53(9), pp.3225-3237.

3.Wang, J. et al. (2013). New Carbon Allotropes with Helical Chains of Complementary Chirality Connected by Ethene-type π-Conjugation. Sci Rep.. 3, 3077.

4.Rowland,R.S et al. (1996). Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. J. Phys. Chem. 100 (18), 7384–7391.

Rep:Mod:AO1995

2015-12-03T21:25:50Z

Ao2013: /* Comparsion between endo and exo */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====
....

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction.The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions from the through space interaction although it is very weak. This indicates that the reason as to why the transition state is lower in energy is due to predominately due to sterics and not the secondary orbital effect in this optimisation. The lack of Secondary orbital effects may be due to the low level of theory used .

Rep:Mod:AO1995

2015-12-03T21:17:32Z

Ao2013: /* Comparsion between endo and exo */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====
....

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-

|}

The following numbering is used for the endo transition structure.

[[Image:ENDONUMBER.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C3-C17(partly formed σ C-C bond)|| 2.16225
|-
|C15-C6 (partly formed σ C-C bond) ||2.16249
|-
|C6-C20 ||2.83099
|-
|C19-C4 ||2.89206
|-

|}

The partially formed is slightly longer for exo and the distance between the carbonyl carbon and the "opposite" carbon appears to be longer for exo. This suggests that there is some steric effect that makes these distances longer. One of the contributons may stem from the H11 and H8 as they point towards the Maleic anhydride in the exo(sp3 hydrised adjacent carbon centre where as the endo has an sp2 hybrised centre).
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking in the reaction.The HOMO of the Endo transition structure shows very little interaction between (C=O)-O-(C=O) and the diene. The overlap with the rest of the molecule is practically non existent. However, there may be contributions form the through space interaction although it is very weak This indicates that the reason as to why the transition state is lower in energy is due to predominsately due to sterics and not the secondary orbital effect in this optimisation.

File:ENDONUMBER.jpg

2015-12-03T20:48:07Z

Ao2013:

Rep:Mod:AO1995

2015-12-03T20:40:39Z

Ao2013: /* Diels alder reaction */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742

|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====
....

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|1
|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
!!Relative energy(kcal/mol)
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|0.68
|}

====Comparsion between endo and exo====

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg|400px|x400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-
|C1-C4|| 1.39749
|-
|C3-C4||1.38185
|-

|}

The following numbering is used for the endo transition structure.

[[Image:Exotsimage.jpg|x400px|400px]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-
|C1-C4|| 1.39749
|-
|C3-C4||1.38185
|-

|}
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking and

The HOMO of the Endo transition structure shows very little contribution from (C=O)-O-(C=O). The overlap with the rest of the ,molecule is practically non existent. This indicates that the reason as to why the transition state is lower in energy is mainly due to steric effect and is not from the secondary orbital effect.

Rep:Mod:AO1995

2015-12-03T20:29:18Z

Ao2013: /* Endo Transition State Optimisation */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====
....

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 and B3YLP/6-31G* using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]] and [[Media:631GD TSBERNY EXO.LOG|B3YLP/6-31G* ]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
!
!
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>631GD TSBERNY EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -448.26
| -612.67933542
|
|}

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027|| 2.27222
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038|| 2.27222
|-
|C2-C20 ||2.94494||1.38601
|-
|C19-C1 ||2.94543||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:ENDOMOHOMO.jpg|x400px|400px]]
|
|}

The following numbering is used for the eno transition structure.

[[Image:Exotsimage.jpg]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038
|-
|C2-C20 ||2.94494
|-
|C19-C1 ||2.94543
|-
|C1-C4|| 1.39749
|-
|C3-C4||1.38185
|-

|}
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking and

The HOMO of the Endo transition structure shows very little contribution from (C=O)-O-(C=O). The overlap with the rest of the ,molecule is practically non existent. This indicates that the reason as to why the transition state is lower in energy is mainly due to steric effect and is not from the secondary orbital effect.

File:ENDOMOHOMO.jpg

2015-12-03T20:25:28Z

Ao2013:

Rep:Mod:AO1995

2015-12-03T20:23:58Z

Ao2013: /* Endo Transition State Optimisation */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====
....

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 and B3YLP/6-31G* using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]] and [[Media:631GD TSBERNY EXO.LOG|B3YLP/6-31G* ]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
!
!
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>631GD TSBERNY EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -448.26
| -612.67933542
|
|}

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027|| 2.27222
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038|| 2.27222
|-
|C2-C20 ||2.94494||1.38601
|-
|C19-C1 ||2.94543||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the TS berney method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|
|}

The following numbering is used for the eno transition structure.

[[Image:Exotsimage.jpg]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027|| 2.27222
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038|| 2.27222
|-
|C2-C20 ||2.94494||1.38601
|-
|C19-C1 ||2.94543||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking and

The HOMO of the Endo transition structure shows very little contribution from (C=O)-O-(C=O). The overlap with the rest of the ,molecule is practically non existent. This indicates that the reason as to why the transition state is lower in energy is mainly due to steric effect and is not from the secondary orbital effect.

Rep:Mod:AO1995

2015-12-03T20:19:53Z

Ao2013: /* Endo Transition State Optimisation */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====
....

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 and B3YLP/6-31G* using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]] and [[Media:631GD TSBERNY EXO.LOG|B3YLP/6-31G* ]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
!
!
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>631GD TSBERNY EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -448.26
| -612.67933542
|
|}

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027|| 2.27222
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038|| 2.27222
|-
|C2-C20 ||2.94494||1.38601
|-
|C19-C1 ||2.94543||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}

====Endo Transition State Optimisation====

The transition state was optimised with both AM1 and B3YLP/6-31G* using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1_BERNEY_ENDO.LOG| AM1]] and [[Media:631GD TSBERNY EXO.LOG|B3YLP/6-31G* ]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1_BERNEY_ENDO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
!
!
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>631GD TSBERNY EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -448.26
| -612.67933542
|
|}

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027|| 2.27222
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038|| 2.27222
|-
|C2-C20 ||2.94494||1.38601
|-
|C19-C1 ||2.94543||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking and

The HOMO of the Endo transition structure shows very little contribution from (C=O)-O-(C=O). The overlap with the rest of the ,molecule is practically non existent. This indicates that the reason as to why the transition state is lower in energy is mainly due to steric effect and is not from the secondary orbital effect.

File:AM1 BERNEY ENDO.LOG

2015-12-03T20:14:47Z

Ao2013:

Rep:Mod:AO1995

2015-12-03T20:13:27Z

Ao2013: /* Exo Transition State Optimisation */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====
....

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 and B3YLP/6-31G* using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]] and [[Media:631GD TSBERNY EXO.LOG|B3YLP/6-31G* ]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
! HOMO
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
| -0.05041976
|[[Image:HOMOEXO.jpg|x500px|500px]]
|
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees
!
!
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>631GD TSBERNY EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -448.26
| -612.67933542
|
|}

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C6-C17(partly formed σ C-C bond)|| 2.17027|| 2.27222
|-
|C15-C3 (partly formed σ C-C bond) ||2.17038|| 2.27222
|-
|C2-C20 ||2.94494||1.38601
|-
|C19-C1 ||2.94543||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}

====Endo Transition State Optimisation====

The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking and

File:HOMOEXO.jpg

2015-12-03T20:05:50Z

Ao2013:

File:AM1 QS2 EXO.chk

2015-12-03T19:51:16Z

Ao2013:

Rep:Mod:AO1995

2015-12-03T19:28:38Z

Ao2013: /* Exo Transition State Optimisation */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====
....

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 and B3YLP/6-31G* using the QST2 method. The log files of the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]] and [[Media:631GD TSBERNY EXO.LOG|B3YLP/6-31G* ]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>AM1 QS2 EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -812.32
|-0.05041976
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>631GD TSBERNY EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -448.26
| -612.67933542
|}

The following numbering is used for the exo transition structure.

[[Image:Exotsimage.jpg]]

====Endo Transition State Optimisation====

The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking and

File:Exotsimage.jpg

2015-12-03T19:27:42Z

Ao2013:

Rep:Mod:AO1995

2015-12-03T19:08:38Z

Ao2013: /* Diels alder reaction */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

==== Regioselectivity of Diels alder reactions====
....

====Exo Transition State Optimisation====
The transition state was optimised with both AM1 and B3YLP/6-31G*. The log files pf the optimsation can be found here. [[Media:AM1 QS2 EXO.LOG| AM1]][[Media:631GD TSBERNY EXO.LOG|B3YLP/6-31G* ]]
The exo transition state was optimised with AM1 semi empirical method and B3YLP
====Endo Transition State Optimisation====

The Secondary orbital overlap effect refers the interaction between orbitals that do not directly participate in the bond forming and breaking and

File:631GD TSBERNY EXO.LOG

2015-12-03T19:08:12Z

Ao2013:

File:AM1 QS2 EXO.LOG

2015-12-03T19:07:39Z

Ao2013:

Rep:Mod:AO1995

2015-12-03T18:47:40Z

Ao2013: /* Optimisation of the ethylene+cis butadiene transition structure */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Atom!! AM1 Bond Lengths (Å)!!6-31G* Bond Lengths (Å)
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}
The typical C-C bond length for sp3 and sp2 are 1.54 and 1.46 Å respectively while the Van der waals radius is 1.7 Å. For both levels of theory, the distance between the carbons where the bonds are formed is less than 3.4 Å( 2 times the van der waals radius) indicating that there is an attractive interaction leading to the sigma bond formation which is consistent with the reaction.

The bond lengths are approximately the same for both basis set used. However, the partly formed sigma C-C bond differ by approximately 0.16 Å.

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T18:32:43Z

Ao2013: /* Optimisation of the ethylene+cis butadiene transition structure */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

{| class="wikitable"
!Bond!! AM1!!6-31G*
|-
|C10-C3|| 2.11922|| 2.27222
|-
|C7-C2 ||2.11935|| 2.27222
|-
|C7-C10 ||1.38290||1.38601
|-
|C1-C2 ||1.38184||1.38306
|-
|C1-C4|| 1.39749||1.40715
|-
|C3-C4||1.38185||1.38306
|-

|}

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T15:48:58Z

Ao2013: /* Optimisation of the ethylene+cis butadiene transition structure */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

This was also optimised with B3LYP/6-31G* and the log file can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_631GD_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| B3LYP/6-31G*
| -525.36
| -234.54389742
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

File:27 11 2015 OPT BERNY DIELSALDERS 631GD PARTB FINALFINAL.LOG

2015-12-03T15:41:48Z

Ao2013:

Rep:Mod:AO1995

2015-12-03T15:39:57Z

Ao2013: /* Optimisation of the ethylene+cis butadiene transition structure */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{4}</math> and<math>\pi^{2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.

The labelling of the transition structure uses the following labels:

[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T15:33:16Z

Ao2013: /* Optimisation of the ethylene+cis butadiene transition structure */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <math>\pi^{-4}</math> and<math>\pi^{-2}</math> components react in a superfacial manner and hence this reaction is thermally allowed.
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T15:29:30Z

Ao2013: /* Optimisation of the ethylene+cis butadiene transition structure */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed.

The Homo and Lumo of ethylene+cis butadiene transition structure is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

The HOMO of butadiene and LUMO of ethene were used to form this transition structure MO.This was deduced by making a direct comparison between the MO of the reactants and the transition structure. Using the woodward Hoffman rule, It can be deduced that both the <matħ> \pi^̣̣̣̪{4} <math>
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T15:22:03Z

Ao2013: /* Optimisation of the ethylene+cis butadiene transition structure */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration corresponding to reaction path at the transition state is shown below.

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration shows that the formation of the bonds are synchronous as the vibration shows both bonds being formed at the same time.

.The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the formation of the sigma C-C bonds as the vibration does not occur in the direction of where the bonds are formed

The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T15:12:23Z

Ao2013:

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====Optimisation of the ethylene+cis butadiene transition structure====
The transition structure was constructed by first building a bicyclo[2,2,2]octane and then removing -CH2-CH2- fragment. The distance between the carbons where sigma bonds are formed are set to 1.5Å. This structure was then optimised with AM1 semi-empirical molecular orbital method using TS Ts berney. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration is shown below

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]
The vibration shows that the formation of the bonds are synchronous. The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the bonding as the vibration does not occur in the direction of where the bond is formed. indicates that at the transition state, it is stable with respect to this normal mode.

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T13:34:43Z

Ao2013: /* Diels alder reaction between ethene and butadiene */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====optimisation of cyclohexene's transition structure====
was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration is shown below

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]
The vibration shows that the formation of the bonds are synchronous. The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the bonding as the vibration does not occur in the direction of where the bond is formed. indicates that at the transition state, it is stable with respect to this normal mode.

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T13:33:54Z

Ao2013: /* optimisation of cyclohexene's transition structure */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Diels alder reaction between ethene and butadiene====

====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====optimisation of cyclohexene's transition structure====
was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration is shown below

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]
The vibration shows that the formation of the bonds are synchronous. The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the bonding as the vibration does not occur in the direction of where the bond is formed. indicates that at the transition state, it is stable with respect to this normal mode.

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T13:30:40Z

Ao2013: /* Optimisation of chair and boat transition state at B3LYP/6-31G* */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}
====Results Table====

Summary of energies (in hartree)

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.71
| align="center" | 44.71
| align="center" | 34.07
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|-
|}

It can be seen from the table above that using B3LYP/6-31G* provides values that are closer to the experimental literature.
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Diels alder reaction between ethene and butadiene====

====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====optimisation of cyclohexene's transition structure====
was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration is shown below

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]
The vibration shows that the formation of the bonds are synchronous. The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the bonding as the vibration does not occur in the direction of where the bond is formed. indicates that at the transition state, it is stable with respect to this normal mode.

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T13:14:00Z

Ao2013: /* Optimisation of chair and boat transition state at B3LYP/6-31G* */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61171063
| align="center" | -234.469219
| align="center" | -234.461869
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.7
| align="center" | 44.7
| align="center" | 34.1
| align="center" | 33.2
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.6
| align="center" | 54.8
| align="center" | 42.0
| align="center" | 41.3
| align="center" | 44.7 ± 2.0
|-
|}
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Diels alder reaction between ethene and butadiene====

====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====optimisation of cyclohexene's transition structure====
was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration is shown below

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]
The vibration shows that the formation of the bonds are synchronous. The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the bonding as the vibration does not occur in the direction of where the bond is formed. indicates that at the transition state, it is stable with respect to this normal mode.

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T12:52:02Z

Ao2013: /* Optimisation of chair and boat transition state at B3LYP/6-31G* */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.692174743
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611711664
| align="center" | -234.469215
| align="center" | -234.461867
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.7
| align="center" | 44.7
| align="center" | 34.1
| align="center" | 33.2
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.6
| align="center" | 54.8
| align="center" | 42.0
| align="center" | 41.3
| align="center" | 44.7 ± 2.0
|-
|}
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Diels alder reaction between ethene and butadiene====

====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====optimisation of cyclohexene's transition structure====
was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration is shown below

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]
The vibration shows that the formation of the bonds are synchronous. The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the bonding as the vibration does not occur in the direction of where the bond is formed. indicates that at the transition state, it is stable with respect to this normal mode.

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

Rep:Mod:AO1995

2015-12-03T12:49:16Z

Ao2013: /* Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC) */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

====Optimisation of chair and boat transition state at B3LYP/6-31G*====

The Boat and Chair transition state was optimised at a higher level of theory using B3LYP/6-31G*. The results are summerised below and the log files can be found here [[Media:Ao2013G BOAT.LOG| Boat]] [[Media:Ao2013CHAIR PART G.LOG| Chair]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2h
| -234.55698303
| -565.54
|}

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/Cm^-1
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G*
|C2v
| -234.54309307
| -530.30
|}

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932242
| align="center" | -231.466700
| align="center" | -231.461341
| align="center" | -234.55698303
| align="center" | -234.414929
| align="center" | -234.409009
|-
| '''Boat TS'''
| align="center" | -231.60280200
| align="center" | -231.450928
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402343
| align="center" | -234.396008
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.692174743
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611711664
| align="center" | -234.469215
| align="center" | -234.461867
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Experimental.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)/kcal/mol'''
| align="center" | 45.7
| align="center" | 44.7
| align="center" | 34.1
| align="center" | 33.2
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)/kcal/mol'''
| align="center" | 55.6
| align="center" | 54.8
| align="center" | 42.0
| align="center" | 41.3
| align="center" | 44.7 ± 2.0
|-
|}
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Diels alder reaction between ethene and butadiene====

====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====optimisation of cyclohexene's transition structure====
was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration is shown below

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]
The vibration shows that the formation of the bonds are synchronous. The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the bonding as the vibration does not occur in the direction of where the bond is formed. indicates that at the transition state, it is stable with respect to this normal mode.

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

File:Ao2013G BOAT.LOG

2015-12-03T12:26:15Z

Ao2013:

Rep:Mod:AO1995

2015-12-03T09:56:56Z

Ao2013: /* Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC) */

== Introduction ==

The transition state of a chemical reaction is the point of highest energy(the least stable point)during the reaction. In other words, It is the point at which the first derivative of energy with respect to { ] is equal to 0 and the second derivative is less than 0.
These structures can not be experimentally determined.
however ,by the use of computational methods, the transition structures can be predicted.
Molecules were optimised using different basis sets.
basis sets are...

== The Cope Rearrangement ==
'''Background'''

The cope rearrangement of 1,5-hexadiene undergoes a [3,3]-sigmatropic shift rearrangement. From woodward hoftman rules,, This can proceed either via a boat or chair transition state.

=====Optimisation of 1,5-hexadiene conformers at HF/3-21G level of theory.=====

1,5-hexadiene with an"anti"linkage,where the two alkene groups are antiperiplanar to each other as shown from the newman projection in figure 1, was drawn in gaussview by setting the dihedral angle to 180<sup>o</sup> The molecule was then optimised with HF/3-21G level of theory. The energy and point group were found to be -231.69253528 a.u and Ci which corresponds to anti2 in the appendix.

[[Image:Antilinkage of 1,5 hexadiene.PNG]]

The "Gauche" conformer of 1,5-hexadiene was drawn in Gaussview by setting the dihedral angle to 60 <sup>o</sup>.Again, this conformer was optimised with HF/3-21G level of theory. The energy point group were found to be -231.69266120 a.u and C<sub>1</sub> respectively. This corresponds to gauche3 in the appendix 1.

One may expect that the most stable conformer to be the anti 1,5-hexadiene conformer . However, the most stable conformer was shown to be the gauche linkage conformer which is due to favourable interactions between both of the <math>\pi</math> orbitals resulting in a greater stabilisation compared to the anti. It can be seen from the HOMO of the gauche conformer that there is secondary orbital interaction between the two <math>\pi</math> bonds whereas the anti does not have that interaction therefore the stabilization lowers the energy.
[[File:Ao2013 AntiMOparta.jpg|thumb|Figure 6:The HOMO molecular orbital of the anti conformer of 1,5 hexadiene at HF/3-21G level of theory ]]
[[File:Ao 2013GaucheMOparta.jpg|thumb|Figure 7:The HOMO molecular orbital of the gauche conformer of 1,5 hexadiene at HF/3-21G level of theory ]]

=====Optimisation of "anti2" 1,5-hexadiene at B3LYP/6-31G* level of theory.=====

The optimisation of anti conformer was done with the B3LYP/6-31G* basis set. The energy was found to be -234.61171063 The point group remains the same but the energies are different due to the different basis sets used and hence cannot be compared. The log file can be found [[Media:AO2013_REACT_ANTI_631_G.LOG| here]].

{| class="wikitable"
!Conformer
!Optimised structure
!Level of theory
!Point group
!Energy/ Hartrees
!Relative Energy/Kcal/mol
!Log file
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_REACT_ANTI_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>1</sub>
!-231.69253528
!0.08
|[[Media:AO2013_REACT_ANTI.LOG| anti]]
|-
|Gauche
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao_2013REACT_GAUCHE_image.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''HF/3-21G'''
|C<sub>i</sub>
!-231.69266120
!0.00
|[[Media:AO2013_REACT_GAUCHE.LOG| gauche]]
|-
|Anti periplanar
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_REACT_ANTI_631_G.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|'''B3LYP/6-31G*'''
|C<sub>i</sub>
!-234.61171063
!-
|[[Media:AO2013_REACT_ANTI_631_G.LOG| anti1]]
|-

The numbering of atoms is shown from the image below.
[[Image:Anti_labelling_scheme.tif|400px|x400px]]
Both basis sets used had the same point group(Ci) indicating that the overall geometry remains practically the same. However, a few difference were observed.

{| class="wikitable" border="1"
! !! colspan="2" | Bond Lengths (Å)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C1-C2 || 1.33350 || 1.31613
|-
| C2-C3 || 1.50419 || 1.50891
|-
| C3-C4 || 1.54816 || 1.55275

|}
The singles bonds for the B3LYP/6-31G* basis set used appear to be longer than the HF/3-21G (C2-C3 and C3-C4) . The double bond appears to be shorter and closer to the literature value of 1.33 Å in the case of B3LYP/6-31G* (C1-C2) compared to HF/3-21G basis set used indicating that B3LYP/6-31G* models the system more accurately.

{| class="wikitable" border="1"
! !! colspan="2" | Dihedral Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C3-C4-C5 || 180 || 180
|-
|}
The dihedral angle between C2-C3-C4-C5 should be 180° as the two alkene groups are anti to each other. Both basis sets were consistent with this value.

{| class="wikitable" border="1"
! !! colspan="2" | Angle (°)
|-
! Atoms !! B3LYP/6-31G* !! HF/3-21G
|-
| C2-C1-H15 || 121.86525 || 121.86752
|-
| C2-C1-H16 || 121.65898|| 121.82269
|-
| H15-C1-H16 || 116.47521|| 116.30950
|-
|}

Since C2 atom is <math>sp^2</math> hybridised ,the angle for C2-C1-H15 , C2-C1-H16 , H15-C1-H16
should be 120°. It can be seen that for B3LYP/6-31G* that these values are closer compared to HF/3-21G used.

Overall, it can be seen that the geometry is almost the same for both basis sets used but the B3LYP/6-31G* basis set is slightly more accurate than HF/3-21G.

===== Frequency analysis of an anti 1,5-hexadiene conformer =====

All of the vibrations were positive and no imaginary frequencies were present indicating that the structure was successfully optimised. The presence of an imaginary frequency is characteristic of the transition state.This occurs the 2nd derivative is a negative value( maximum provided 1st derivative is 0) implying a negative force constant due to the relationship as shown by the following quantum harmonic oscillator equation:
<math> \nu{_{cm^{-1}}}=\frac{1}{2\pi c} \sqrt{\frac{k}{\mu}} </math>
where c represents the speed of light in Cm s<sup>-1</sup>, k represents the force constant in gs^-2, and μ the reduced mass in grams.
The log file can be found [[Media:_REACT_ANTI_631_G_FREQ.LOG| here]]
It is also possible to obtain the thermochemistry data which is shown in the following table.

{| class="wikitable"
!Energetic Values!!
|-
|Sum of Electronic and Zero-point Energies at 0 K || -234.469219
|-
|Sum of Electronic and Thermal Energies at 298.15 K || -234.461869
|-
|Sum of Electronic and Thermal Enthalpies||-234.460925
|-
|sum of Electronic and Thermal Free Energies||-234.500809
|}

The sum of electronic and zero-point energies at 0 K refers to the sum of the electronic potential energy and the zero point energy in the system The sum of electronic and thermal energies at 298.15 K at 1 atm is a sum of the electronic,translational,rotational and vibrational energies. The sum of electronic and thermal enthalpies contains a RT correction term(H = E + RT). The sum of electronic and thermal free energies contains an entropic contribution (G = H - TS).

=====Optimizing the "Chair" and "Boat" Transition Structures=====

=====Optimisation of allyl fragment=====

In order to make the transition states of the chair and boat conformation, it is possible to build the transition state from smaller fragments and so an ally fragment was used. This was optimised with the HF/3-21G basis set. and the file can be found [[Media:AO_2013ALLYL_FRAGMENT.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

'''Optimisation of 1,5-hexadiene Chair Transition State by using TS Berny Method and HF/3-21G theory (Guess method)'''

The Transition state was built by placing an optimised ally fragment on top of another ally fragment in a 'staggered' conformation.The distance between the terminal carbons of the allyl fragments was set to 2.2 Å . The structure was then optimised using the Berney algorithm The results are summerised below and the log file can be found [[Media:TSberny321Gchair.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Image_321g_Tsbernychair_actual.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932242
| -817.93
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.25;vibration 1;</script>
<uploadedFileContents>TSberny321Gchair.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Optimisation of 1,5-hexadiene Chair Transition State by using frozen coordinate method and HF/3-21G theory=====

The chair conformation can also be optimised by another method called the frozen coordinate method. The structure was optimised with HF/3-21G where the distances between the terminal carbons of the allyl fragments were fixed to 2.2 Å(where the bonds break and form ). This means that the optimisation proceeded with the terminal carbons being fixed while the rest of the molecule is optimised. The terminal carbons were then unfixed and the whole molecule was reoptimised. The optimised file can be found[[Media:Ao2013PARTD_FREQCHAIR.LOG| here]].
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013partdimage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C1
| -231.61932233
| -817.89
|}

A imaginary frequency was found with a wavenumber of-817.93<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.19;vibration 1;</script>
<uploadedFileContents>Ao2013PARTD_FREQCHAIR.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

{| class="wikitable"
!Method!!Bond breaking length/Å!!bond forming length/Å
|-
|Guess with berney||1.38927 || 2.02055
|-
|Frozen coordinate||1.38929 || 2.02076
|-
|}
Both methods provide very similar energies,bond lengths and imaginary frequencies indicating that both methods can obtain reasonable results. however the Guess method is highly depended on how well the initial structure is drawn so the frozen coordinate method is more reasonable to use.

=====Optimisation of 1,5-hexadiene boat Transition State by using QST2 method and HF/3-21G theory=====

A different method,QST2, is used to optimise the boat transition structure. The transition state is obtained by interpolating between the reactant and product. The labelling of the reactant and product is shown below.

{| class="wikitable"
!Labelling of reactant!!labelling of product
|-
|[[Image:Ao2013Parteboatnumberingimagereactant.jpg|400px|x400px]]||[[Image:ParteboatnumberingimagePRODUCT.jpg|400px|x400px]]
|}
Intially,the anti 2 structure which was used as both the product and reactant from appendix 1 was optimised with HF/3-21G using the QST2 method. However, this lead to a transition structure that was highly unfavorable which is shown below.

|[[Image:Failed transitionstate hahahahahahaahha.jpg|400px|x400px]]||

In order to obtain the correct geometry for the reactant and product, the following torsion angles were applied :C2-C3-C4-C5 was set to 0° in the reactants,C5-C6-C1-C2 was set to 0° in products.Also the following angles were applied: C2-C3-C4 and C3-C4-C5 were set to 100° in the reactant, C5-C6-C1 and C6-C1-C2 were set to 100° in the product . This was then optimised with HF/3-21G using the QST method.The optimisation and frequency output log file for the successful boat transition structure can be found [[Media:Ao2013WORKING_JOB_PART_E.LOG| here]].

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}

A imaginary frequency was found with a wavenumber of-839.94<sup>-1</sup> indicating that the transition state is formed. The vibration is shown below.
<jmol>
<jmolApplet>
<title> Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.41;vibration 1;</script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

====Intrinsic reaction coordinate of chair and boat transition structure at HF/3-21G (IRC)====

In order to confirm that the transition structure has been correctly optimised , It is necessary to check whether or not the reaction path from the transition state goes to both minima in both directions(reactants and production). IRC preforms a series of optimisations on the constrained geometries along the reaction path (steepest decent which is from the transition state to the reactants and products)

The chair transition structure was optimised with HF/3-21G with and IRC. The reaction coordinate was calculated in the forwards direction only because the reaction coordinate is symmetric. The number of points that were monitored was set to 50. The log file can be found [[Media:CHAIR_PART_F.LOG| here]]. The boat IRC can be found [[Media:BOAT_PART_F.LOG| here]]

{| class="wikitable" border="1"
! Chair !! Boat
|-
! [[Image:Ao2013 totalenergyalongirctutorialchair.jpg]] !![[Image:BoatIRCpartfenergy.jpg]]
|-
![[Image:Ao2013chairtutRMS.png]] !![[Image:BoatIRCpartfenergyRMS.jpg]]

|-

|}

|}

It can be seen from the plots of the total energy vs IRC that the energy is initially at it's peak(the transition state) and then decreases till the total energy does not change(reactant/product as the PEs is symmetrical in this case). On the otherhand, the RMS plot displays how the 1st derivative of the total energy varies with IRC.

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
imaginary frequency/Cm
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013CHAIR PART G.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|B3LYP/6-31G̈
|C2h
| -234.55698303|}
| 565.54

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013_Image_321g_Tsbernychair.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|C2v
| -115.82304010
|}

{| class="wikitable" border="1"
|-
! ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
! ''' '''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
! width="125" align="center" | '''Electronic energy'''
! width="125" align="center" | '''Sum of electronic and zero-point energies at 0 K'''
! width="150" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932232
| align="center" | -231.466706
| align="center" | -231.461346
| align="center" | -234.55692633
| align="center" | -234.414918
| align="center" | -234.408986
|-
| '''Boat TS'''
| align="center" |-231.60280224
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.54307752
| align="center" | -234.402337
| align="center" | -234.395999
|-
| '''Reactant (''Anti2'')'''
| align="center" | -231.692174743
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611711664
| align="center" | -234.469215
| align="center" | -234.461867
|}

{| class="wikitable" border="1"
|-
! ''' '''
! colspan="2" width="250" align="center" | '''HF/3-21G'''
! colspan="2" width="250" align="center" | '''B3LYP/6-31G*'''
! width="125" align="center" | '''Expt.'''
|-
! ''' '''
! width="125" align="center" | '''0 K '''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
! width="125" align="center" | '''298.15 K'''
! width="125" align="center" | '''0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 44.7
| align="center" | 34.1
| align="center" | 33.2
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 54.8
| align="center" | 42.0
| align="center" | 41.3
| align="center" | 44.7 ± 2.0
|}
HF and DFT
compare geometrys of both basis sets

smaller basis sets are very good at getting the geometry but a larger basis set is need to get to the energy.

====Intrinsic reaction coordinate of chair transition structure at HF/3-21G (IRC)====
It also worth mentioning that the energy obtained from B3LYP/6-31G* would be more accurate as..... The HF/3-21G level of theory is sufficient enough to obtained the correct geometry whereas B3LYP/6-31G* is required for a more accurate representation of the energy.

==Diels alder reaction==
====Background ====
.
.
.
====Diels alder reaction between ethene and butadiene====

====Optimisng cis butadiene with AM1 level of theory====

Cis butadiene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013PARTI_CIS_BUTADIENE.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013PARTI_CIS_BUTADIENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|C2v
| 0.04879719
|}
The Homo and Lumo of cis butadiene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Image butadiene homo antisymettric.jpg|x500px|500px|]] !! [[Image:Ao2013Image butadiene lumo symettric.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}

====Optimising ethene with AM1 level of theory====

Ethene was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:Ao2013ETHENE.LOG| here]]
{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>Ao2013ETHENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
|D2h
| 0.02619024
|}
The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Ao2013Ethenehomo symettric.jpg|x500px|500px|]] !![[Image:Ao2013Ethenelomo antisymettric.jpg|x500px|500px|]]
|-
! The HOMO is symmetric with respect to the plane !! The LUMO is antisymmetric with respect to the plane
|-

|}

====optimisation of cyclohexene's transition structure====
was optimised with the AM1 empirical level of theory. The data is summerised in the following table and the log file for the optimisation can be found [[Media:27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG| here]]

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Imaginary frequency/ cm<sup>-1</sup>
!Energy/ Hartrees

|-
|<jmol>
<jmolApplet>
<title></title>
<color>white</color>
<size>200</size>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|AM1
| -956.15
| 0.11165465
|}
The imaginary frequency vibration is shown below

<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.77;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The Homo and Lumo of ethene is shown below.
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
! [[Image:Homoimagets.jpg|x500px|500px|]] !![[Image:Ao2013Lumoimagets.jpg|x500px|500px|]]
|-
! The HOMO is antisymmetric with respect to the plane !! The LUMO is symmetric with respect to the plane
|-

|}
The labelling of the transition structure uses the foloowing labels:
[[Image:Ao2013Number of tansitionstate cyclo.jpg|x400px|400px|]]
The vibration shows that the formation of the bonds are synchronous. The lowest positive frequency was calculated to be 177.19 cm<sup>-1</sup> The vibration of the lowest positive frequency is shown below.
<jmol>
<jmolApplet>
<title>Animation of imaginary frequency</title>
<color>white</color>
<size>250</size>
<script>frame 1.78;vibration 1;</script>
<uploadedFileContents>27_11_2015_OPT_BERNY_DIELSALDERS_PARTB_FINALFINAL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration appears to not have any relation to the bonding as the vibration does not occur in the direction of where the bond is formed. indicates that at the transition state, it is stable with respect to this normal mode.

====cyclohexa-1,3-diene reaction with maleic anhydride====

{| class="wikitable"
!Optimised Structure
!Level of Theory
!Point Group
!Energy/ Hartrees
!Imaginary frequency/cm<sup>-1</sup>
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2;rotate x -20; </script>
<uploadedFileContents>Ao2013WORKING_JOB_PART_E.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|HF/3-21G
|Cs
| -231.60280200
| -839.94
|}
====Exo Transition State Optimisation====
====Endo Transition State Optimisation====
====cyclohexa-1,3-diene reaction with maleic anhydride====

File:Ao2013CHAIR PART G.LOG

2015-12-03T09:54:06Z

Ao2013: