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=Cope Rearrangement of 1,5-hexadiene=
the Cope Rearrangment of 1,5-hexadiene is classified as [3,3]sigmatropic rearrangement and is widely studied. The mechanism of the rearrangement is thought to occur via either the chair-like structure or the boat-like structure transition states in concerted manner.  The exercise aims to find the structures of the transition states and their energies on the potential surface using Gaussian calculation and the next section shows optimisations using '''Gauss''' to find structures of reactants( as well as product in this case) which are minimum in energy, ie the conformers of 1,5-hexadiene. 
==Optimising the Reactants and Product==
the following table shows the various conformers of the 1,5-hexadiene, with their relative energies as compared to the lowest. 
{| class="wikitable"
|+ Table of gauche conformers and their relative energies
! '''structure No.'''  !! Caluclated Energy/ Hatrees (HF/3-21G)||'''Relative Energy with the lowest''' ||Point Group||Image||Description

|-
| '''Gauche No.2''' || -231.69266||'''0'''||C1||<jmol><jmolApplet><title>1,5-Hexadiene gauche No.2</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Hexadiene gauche 2.mol</uploadedFileContents>
</jmolApplet></jmol>||Gauche structure No.2 is the global minimum state, whereby the dihedral angles are 120 degree between bond C12-C14 and bond C6-C9, 60 degree in the central and 120 degree between bond C1-C4. C1 point group.
|-
| '''Gauche No.7''' || -231.69167||'''0.62'''||C2||<jmol><jmolApplet><title>1,5-Hexadiene gauche No.7</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Hexadiene gauche 7.mol</uploadedFileContents>
</jmolApplet></jmol>||Gauche structure No. 7 has the angle between bond C7-C9 and bond C1-C4 being 124 degree, 60 degree for the two central carbons and the angle between bond C1-C4 and bond C12-C14 being 124. It is in C2 point group.
|-
| '''Gauche No.6''' ||-231.69153||'''0.71'''||C2||<jmol><jmolApplet><title>1,5-Hexadiene gauche No.6</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Hexadiene gauche 6.mol</uploadedFileContents>
</jmolApplet></jmol>||corresponding to gauche structure 6, the dihedral angle between bond C12-C14 and bond C6-C9 is 109 degree, 60 degree for two central carbons and 109 degree between bond C6-C9 and bond C1-C4, It is in C2 point group.
|-
| '''Gauche No.8''' ||-231.68962||'''1.91'''||C1||<jmol><jmolApplet><title>1,5-Hexadiene gauche No.8l</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Hexadiene gauche 8.mol</uploadedFileContents>
</jmolApplet></jmol>||corresponding to gauche structure 5 on the table: the dihedral angles are 121 degree between bond C1-C4 and bond C6-C9, 60 degree for central carbon and 14 degree between bond C6-C9 and bond C12-C14, it is C1 point group.
|}


The following table shows the calculated energy and relative energies of different anti conformers.

{| class="wikitable"
|+ Table of anti conformers and their relative energies
! '''structure No.'''  !! Caluclated Energy/ Hatrees ('''HF/3-21G''')||'''Relative Energy with the lowest''' ||Point Group||Image||Description
|-
| '''anti No.1''' || -231.69260||'''0.04'''||C2||<jmol><jmolApplet><title>1,5-Hexadiene anti No.1</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Hexadiene anti 1.mol</uploadedFileContents>
</jmolApplet></jmol>||for anti No.1, dihedral angles are 65 degree between bond C12-C14 and C6-C9, 180 degree in the centre and 65 degree between bond C6-C9 and bond C1-C4, it has point group of C2.
|-
| '''anti No.2''' || -231.69254||'''0.08'''||C<sub>i</sub>||<jmol><jmolApplet><title>1,5-Hexadiene anti No.2</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Hexadiene anti 2.mol</uploadedFileContents>
</jmolApplet></jmol>||for anti No.2, the dihedral angles are 114 degree between C1-C4 and bond C6-C9, 180 degree in the central and 114 degree between bond C6-C9 and bond C12-C14, it has the point group of C<sub>i</sub>. 
|}

Generally the anti structures are more stable than gauche conformers, as the two alkene groups are furthest apart to eliminate steric reason. However, the global minimum corresponds to [[Gauche No.2]], which could be due to the adhesion effect of the two H atoms within range of the covalent radii.<reference>1</reference>


For the same structure of anti No.2, using different calculation method of '''B3LYP/6-31G*''', energy of '''-231.5597 Ha''' is obtained. Meanwhile the structure underwent slight structural conformation, in which the dihedral angle between C1-C4 bond and C6-C9 bond changed from 114 to 118.8 degree and the same change occurred for bond C6-C9 and C12-C14. however the overall geometry did not change as it remains C<sub>i</sub> as seen below, as well as an expected IR spectrum for this structure.
{|class="wikitable"
|-
|<jmol><jmolApplet><title>1,5-Hexadiene anti No.2 (6-31G*)</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Hexadiene anti 2 -B3LYP- zw.mol</uploadedFileContents>
</jmolApplet></jmol>||[[File:Anti 2 IR spectrum.jpg|centre]]
|}


Table below shows the comparison of energies calculated using two different methods for the same structure of '''anti No.2'''

{| class="wikitable"
|+ Table of energies of comparison of energies of two methods
! type of energies  !! Caluclated Energy/Hatrees ('''HF/3-21G''')!! Caluclated Energy/Hatrees ('''B3LYP/6-31G*''')

|-
| Sum of electronic and zero-point Energies || -231.53954||-234.418888
|-
| Sum of electronic and thermal Energies || -231.53257||-234.412239
|-
| Sum of electronic and thermal Enthalpies ||-231.53162||-234.411294
|-
| Sum of electronic and thermal Free Energies ||-231.57092||-234.449554
|}



==Optimising the Chair and Boat Transition Structures==

Three methods are used in finding the transition state of the Cope rearrangement, which can occur via either chair-like transition state or boat-like transition state.
[[File:Chair-boat ts.gif|frame|centre|Transition states of Cope Rearrangement]]

===Chair Transition State===
====HF3-21G (Hessian) method====
Allyl fragments which are the components that make up the transition states are drawn and optimised at '''HF/3-21G''' level of theory,with force constant being calculated (the Hessian), two of the fragments are arranged in the chair-liked orientation, and the distances between the terminal carbons are set to at 2.2 Å. The guess-ed transition structure is then put to calculation of '''frequency and optimisation'''with force constant being calculated (the Hessian). The result of the electronic energy is '''-231.61932Ha''' and calculation of frequency and optimisation shows an imaginary frequency of -818.00 cm <sup>-1</sup> and is corresponding to the Cope Rearrangement as shown by the animation below, as well as a predicted IR spectrum for this transition structure.
{|class="wikitable"
|-
|[[File:Chair ts(-808).gif|1200px|animation of bond formation in transition state]]||[[File:Chair ts.jpg|expected IR spectrum for chair-like transition state]]
|}

The previous step is repeated using the '''B3LYP/6-31G*''' level of theory and carried out frequency calculations as well. The electronic energy calculated was '''-234.55698Ha''' and an imaginary frequency at -566 cm<sup>-1</sup>. The geometry and spacial arrangement are very similar,but there is significant energy differences.

====Freezing coordinate method====
this method involves using Redundant Coord Editor to freeze the bond lengths of the newly formed σ C-C bonds to be 2.2 Å.
By freezing the coordinates, the optimisition (HF/3-21G)calcultion shows the structure of the transition state to be the same as above, with the bond lengths fixed at 2.2 Å, as shown below.
<jmol><jmolApplet><title>Chair-like transition state</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair ts modredundant -force constant 1-.mol</uploadedFileContents></jmolApplet></jmol>

The structure was reoptimised using a normal guess Hessian modifying the two differentiating coordinates which correspond to the two forming σ C-C bonds.The result is shown below.
<jmol><jmolApplet><title>Chair-like transition state</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Chair ts modredundant -force constant 1-.mol</uploadedFileContents></jmolApplet></jmol>
the Transition state is then optimised and the energy obtained is the same as before which is  '''-231.61932Ha'''. the two methods produced the same transition state with the energy, showing both are effective, because the guessed structure is very close to the "real" transition state structure brought out by calculation. 

===Boat Transition Structure===
====QTS2 method====
In finding the boat-like transition structure, the QST2 method is used. In this method, the structure of the reactant and product are drawn and the software is set to compute the transition structure between the two structures drawn. In this case, the reactant and the product are the same, therefore the atoms must be labeled for the software to recognise the starting point and end point of the reaction.
Using the QST2 calculation, first the structure of the reactant and product are drawn as shown below, the labeling on the atoms are to show there is rearrangement.
[[File:Reactant product.png|1300px|frame|centre|Labeling of reactant and product]]

However, after the calculation, a Chair-like Transition structure is present as shown below, and this is due to the limitation of the software in which the rotation around the central bond is not taken into consideration.
<jmol><jmolApplet><title>Chair-like transition state using QTS2</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>Boat QST2 (failed).mol</uploadedFileContents></jmolApplet></jmol>

To avoid this limitation, the central bond are manually rotated in the product structure as shown below.
[[File:Boat QST2 suc.png|1300px|frame|centre|Labeling of reactant and product]]
and the transition structure obtained using this method is the boat conformer.
<jmol><jmolApplet><title>boat-like transition state using QTS2</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>Boat TS.mol</uploadedFileContents></jmolApplet></jmol>

===Intrinsic Reaction Coordinate=== 
IRC method is used to determine which of the 1,5-hexadiene conformers the reaction follows as well as the pathway the reaction has taken via the chair-like transition state. Since the reaction is symmetrical, only the forward reaction going from the transition state to the product is shown. This result in the gauche 2 structure as on the Appendix I <ref>https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3</ref> or gauche No.7 as in table I shown above.

{| class="wikitable"
|-
| [[File:IRC forward coordinate.gif|upright=2|center|animation of reaction from transition to product]] || [[File:Chair ts IRC.png|upright=2]]
|}

However this structure is not the minimum geometry, evident from table I. The IRC calculation is repeated with 150 points with force constant calculated at every step, aiming to find the structure with minimum energy, yet the result obtained is the same as before. An explanation is that the intrinsic reaction coordinate shows only the pathway with the deepest gradient,and this pathway may not be the same as the pathway that leads to a global minimum, or the transition state used would only lead the product shown, and other minimum structure must formed via different transition state. Therefore, conformer analysis must be conducted for future experiments.

==Activation Energies==
Below is the summary of activation energies calculated based on the total energies computed by Guassian using two different level of theory. The reactant is selected as the anti 2 conformer. 
{| class="wikitable"
|+ Table the activation energies
! scope="col" |
! scope="col" | '''HF/3-21G''' at 0K
! scope="col" | '''HF/3-21G''' at 298.15K
! scope="col" | '''B3LYP/6-31G*''' at 0K
! scope="col" | '''B3LYP/6-31G*''' at 298.15K
! scope="col" | Expt. at 0K
|-
| '''ΔE (chair)''' in kcal/mol||45.71||44.70||34.05||33.16||33.5 ± 0.5
|-
| '''ΔE (boat)''' in kcal/mol||55.60||54.76||41.96||41.32||44.7 ± 0.5
|}

The chair transition structure has lower activation energy, hence conformers formed via the chair-like transition state are the kinetic product.It is also observed that '''B3LYP/6-31G*''' level of theory at 0K gives better result as the values are closer to the experimental.


=The Diels-Alder Cycloaddition=
The Diels-Alder cycloaddition is a concerted pericyclic addition, this reaction occurs via formation of new and stronger σ bond from two overlapping p orbitals by breaking weaker π bonds. The reaction is allowed only when there are good overlap between the orbitals with the right symmetry. 

==Cis Butadiene and ethene==
<center>[[File:Cis but.gif|500px|center|thumb|''The prototype reaction between butadiene and ethene'']]</center>

===Experimental===
The HOMO and LUMO of cis butadiene are shown below
{| class="wikitable"
|+Plot of Orbitals of cis butadiene
|-
| HOMO ||[[File:Cis butadiene HOMO.png|thumb]]||anti-symmetrical
|-
| LUMO ||[[File:Cis butadiene LUMO.png|thumb]]||symmetrical
|}


the guessed transition state structure for this cycloaddition is drawn on the assumption that the transition structure is very similar to the final product, using Hammond's postulate <ref>Anslyn, Eric V.; Dougherty, Dennis A. (2006). Modern Physical Organic Chemistry. Sausalito, CA: University Science.</ref> , therefore the guessed structure is drawn by removing the two newly formed σ C-C bonds. The structure is then optimised to a transition state (Berny) using HF/3-21G level of theory as it is the quickest method to do. The transition state is then obtained, as shown below, and it is confirmed via the IRC method and the animation of which is also shown below.

{| class="wikitable"
|+Cis butadiene transition state '''point group C<sub>s</sub>'''
|-
| <jmol><jmolApplet><title>Transition structure</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TS GUESS4.mol
</uploadedFileContents>
</jmolApplet></jmol> || [[File:TS guess 4 TS to product.gif|upright=2]]||[[File:Ts guess 4.png]]
|}

The computation also shows the imaginary vibration frequency of -818.44 cm<sup>-1</sup>, which correspond to the formation of two σ C-C bonds, at the same time, as the terminal carbons are brought in closer by the vibrations allowing the orbitals to overlap. [[File:TS guess 4.gif|1200px|Alt=animation of formation of sigma bonds]]
The next positive vibration correspond to a swinging motion conducted by both molecule in the transition and this vibration does not help in bringing the orbitals closer for addition.

Typical C-C single bond has bond length of 1.20 to 1.50 Å, <ref>Handbook of Chemistry & Physics (65th ed.). CRC Press. ISBN 0-8493-0465-2.</ref> and the old C-C single bonds in this structure have bond lengths of 1.37 Å. the newly partially formed C-C bond has length of 2.20 Å. The van der Waals radius for carbon atom is 1.70Å, therefore the newly forming bonds are within the van der Waals radii of two carbon atoms.


The following table summaries the HOMO and LUMO of the transition structure shown above.
{| class="wikitable"
|+HOMO and LUMO of transition structure
|-
| HOMO of ts ||[[File:TS HOMO zw.png|thumb]]||anti-symmetrical
|-
| LUMO of ts ||[[File:TS LUMO zw.png|thumb]]||symmetrical
|}

==Cyclohexa-1,3-diene with maleic anhydride==
<center>[[File:Part iii.gif|500px|center|thumb|''reaction between Cyclohexa-1,3-diene and maleic anhydride'']]</center>
This reaction forms two products, one called the exo and the other endo. The following sections aim to find the energies differences between the two by finding the transition states, and hence rationalise the ratio in the products formed. 
===Exo Product===

The transition state is determined using similar method as the cis butadiene, using Hammond's Postulate, and the structure is confirmed using IRC running in both direction following 250 points with force constant calculated at every step


{| class="wikitable"
|+ Summary of exo transition state
|-
| <jmol><jmolApplet><title>exo transition state</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CYCLOHEXADIENE WITH MALEIC exo product.mol</uploadedFileContents></jmolApplet></jmol>||[[File:Cyclohexadiene with maleic exo.gif|1200px|exo product formation]]||[[File:Exo pathway zw.jpg]]
|}



{| class="wikitable"
|+ Various measurement of exo transition state
|-
| [[File:Exo product measurements.png|thumb]]||HOMO[[File:Exo ts HOMO.png|thumb]]||anti symmetric
|-
|  ||LUMO [[File:Exo LUMO.png|thumb]]||anti symmetric
|}

By comparing the IRC plot, it is clear the endo transition state has a lower energy compared to the exo by 0.68 Kcal/mol, as both transition states are optimised using HF/3-21G level of theory. Therefore the kinetic product is the endo product, due to lower kinetic barrier.
Endo transition state has lower energy because there are less steric interactions between -(C=O)-O-(C=O)- fragment and the rest of the system.
<ref>uhoadsghfio</ref>

<references/>

===endo product===

This transition state is determined using QTS2 method as described above.TS is confirmed using IRC in both direction following 250 points with force constant calculated at every step.

{| class="wikitable"
|+ summary of endo transition state
|-
| <jmol><jmolApplet><title>endo transition state</title><color>blue</color>
<size>200</size><script>moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Endo product.mol</uploadedFileContents></jmolApplet></jmol>|| [[File:Endo full pathway.gif|1200px]]||[[File:Endo pathway.jpg]]
|-
| [[File:Endo measurements.png|thumb]] ||HOMO [[File:Endo ts HOMO.png|thumb|center]]||antisymmetric
|-
|||LUMO[[File:Endo ts LUMO.png|thumb|centre]]||antisymmetric
|}

Endo transition state is lower in energy by 0.68 Kcal/mol than the exo, thus endo is the kinectic product as the kinectic barrier is lower. Both transition structure is optimised using HF/3-21G level of theory.


References