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==='''The Cope Rearrangement Tutorial'''===

The cope rearrangement is a pericyclic reaction, it is a [3,3] sigmatropic rearrangement of 1,5-dienes. In this experiment the cope rearrangement of 1,5-hexadiene is examined.

'''Optimizing the Reactants and Products'''

Firstly 1,5-hexadiene was drawn in the antiperiplanar conformation and the structure was optimised; giving an energy of -231.69253528 Hartree and a point group Ci/C1 (<span style="color:gray">Which of the two point groups is it?</span> [[User:Jbettenc|João]] ([[User talk:Jbettenc|talk]]) 09:23, 24 March 2015 (UTC)).


Then the gauche linkage of 1,5-hexadiene was drawn and optimised; giving an energy of -231.68302548 Hartree and a point group Cs/C1. Both these energies are very similar with the antiperiplanar conformer being slightly lower in energy, this is what is expected simply judging from sterics.

[[File:Part b syn.jpg| thumb |Figure 1:gauche linkage of 1,5-hexadiene]]


In figure 2 a lower energy gauche conformer can be seen, with an energy of -231.69266122 Hartree. 

[[File:React c.png| thumb |Figure 2:Gauche 3]]

Then anti2 conformation was built and optimised giving an energy of  -231.69253510 Hartree and a point group Ci - seen figure 3. The value given for the energy of this conformer is -231.69254 Hartree, which is the same as the value calculated from Gaussian (to less decimal places).


[[File:Anti2yoyo.jpg| thumb |Figure 3: Anti 2]]

The anti2 conformer was then reoptimised at the B3LYP/6-31G* level giving an energy of -233.33634309 Hartrees. (<span style="color:gray">How does the structure compare to the structure you had optimized before?</span> [[User:Jbettenc|João]] ([[User talk:Jbettenc|talk]]) 09:23, 24 March 2015 (UTC))

[[File:Anti2yoyoDTF.png| thumb |Figure 4: Anti 2 reoptimised at B3LYP/6-31G* level]]

A frequency calculation was then performed on the B3LYP/6-31G* optimised molecule. This confirmed that this is a minimum as all the vibrational frequencies were real and positive.

 i) Sum of electronic and zero-point Energies= -233.192896
 ii)Sum of electronic and thermal Energies= -233.185589          
 iii) Sum of electronic and thermal Enthalpies= -233.184644
 iv) Sum of electronic and thermal Free Energies= -233.224571

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

The boat and chair transition structures of the cope rearrangement are made and optimised so they can be compared. To do this firstly a C3H5 allyl fragment is built and optimised to HF/3-21G level of theory. Then two of these optimised fragments were combined to make a rough guess of what the chair transition state should look like, setting the two fragmetns 2.2 Å apart.

 <jmolFile text="allyl fragment, energy -115.82304010 Hartree, C2v point group">Allylfragment_thu.mol</jmolFile>

This guess was then optimised in two ways. The first was optimising it to a transition state by selecting optimization to a TS (Berny) in the calculate menu.This gave bond forming/bond breaking bond lengths 2.02159 Å and 2.02098 Å, and an energy of -231.61932181 Hartree.
(<span style="color:gray">Did you confirm the structure you obtained was a transition state?</span> [[User:Jbettenc|João]] ([[User talk:Jbettenc|talk]]) 09:23, 24 March 2015 (UTC))
 
 <jmolFile text="Chair, optimised to a TS">Chair_b_thu3.mol</jmolFile>

The next method of optimising the chair transition state was to optimise it using the frozen coordinate method. This involves freezing the allyl fragment bonds that will be made to a set length (2.2 Å) then optimising the structure to a minimum. Then unfreezing the bonds and optimising the structure to a transition state. This method gave bond forming/bond breaking bond lengths 2.02071 Å and 2.02074 Å, and an energy of -231.61932233 Hartree.

 <jmolFile text="Chair, optimised with frozen coordinate method">Chair_opt_d_thu3.mol</jmolFile>

These two method gave very similar results with the frozen coordinate method giving a slight lower energy and short bond lengths.
(<span style="color:gray">Did you confirm the structure you obtained was a transition state?</span> [[User:Jbettenc|João]] ([[User talk:Jbettenc|talk]]) 09:23, 24 March 2015 (UTC))

The QST2 method was used to optimise the boat transition structure. For this two gauche conformers of 1,5-hexadiene were put into GaussView and numbered so they corresponded to the reactant and product of the cope rearrangement. Then the QST2 calculation was run. This gave bond forming/bond breaking bond lengths 2.14181 Å and 2.14046 Å, and energy -231.60280217 Hartree. This is a higher energy and longer bond lengths then the chair transition state, implying that the reaction would prefer to go via the chair transition state. Although, there's not much in it.
(<span style="color:gray">Did you compare with experimental values? Did you see how different levels of theory compare with experimental values?</span> [[User:Jbettenc|João]] ([[User talk:Jbettenc|talk]]) 09:23, 24 March 2015 (UTC))
 
 <jmolFile text="Optimised boat QST2 method">2nd_QST2_thu.mol</jmolFile>

===The Diels Alder Cycloaddition===

GaussView was used to build cis butadiene and then optimized to the HF/3-21G level. The HOMO and LUMO were plotted and it can be seen that both orbitals are asymmetric with respect to the plane. (<span style="color:gray">Indeed they are anti-symmetric with respect to the plane of the molecule, they are π orbitals. What other planes of symmetry are there? Would symmetry with respect to these be important to determine the outcome of the reaction?</span> [[User:Jbettenc|João]] ([[User talk:Jbettenc|talk]]) 09:23, 24 March 2015 (UTC))

[[File:Cisbutadiene.kitts.jpg| thumb |Figure 5: LUMO of cisbutadiene]]
 
[[File:Cisbutadiene HOMO.jpg| thumb |Figure 6: HOMO of cisbutadiene]]

In order to obtain a transition state geometry of the reaction between ethylene and butadiene, firstly a bicyclo system was built in GaussView and optimised to a minimum. Then the CH2CH2 fragment was deleted and the transition state optimised using the frozen coordinate method, setting the interfragment distance originally as 2.2 Å. The transition state had transition bond lengths of 2.200130 Å, this is higher than the Van der Waal radi of carbon atoms (around 1.75 Å<sup>1) - meaning that the bond has not formed. (<span style="color:gray">However, the bosd distance is inferior to twice the van der Waals radius for carbon. Is that significant?</span> [[User:Jbettenc|João]] ([[User talk:Jbettenc|talk]]) 09:23, 24 March 2015 (UTC))
[[File:Guess ts bii.jpg| thumb |Figure 7: Guess of transition state of bicyclo system]]

[[File:TS ii.jpg| thumb |Figure 8: Transition state of ethylene and butadiene]]

[[File:Guess ts ii HOMO.jpg| thumb |Figure 9: HOMO of Diels-Alder Transition State]]

[[File:TS ii LUMO.jpg| thumb |Figure 10: LUMO of Diels-Alder Transition State]]

The HOMO of this transition state can be seen to be symmetrical whilst the LUMO is asymmetrical. (<span style="color:gray">How do these relate to the orbitals of the reactants?</span> [[User:Jbettenc|João]] ([[User talk:Jbettenc|talk]]) 09:23, 24 March 2015 (UTC))

The Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride can potentially give either an endo or an exo product. To examine which would be favoured we can examine the exo and endo transition states, to see which is lower in energy. First, cyclohexa-1,3-diene and maleic anhydride are built and optimised to the  HF/3-21G level. Then these are used to build a rough estimate of the endo and exo transition states. Primarily the endo adduct is given as this is lower in energy (and this reaction is kinetically controlled. 

[[File:Maleic anhydride Cyclohexa-1,3-diene.jpg| thumb |Figure 11: Maleic anhydride (left) and cyclohexa-1,3-diene (right)]]

[[File:Endoexoyo.jpg| thumb |Figure 12: Endo and exo guess transition structures]]

===References===

1.  R. Scott Rowland, Robin Taylor: Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii. In: J. Phys. Chem. 1996, 100, S. 7384–7391, doi:10.1021/jp953141+.