ChemWiki - User contributions [en]

Rep:Mod:tf910

2013-03-15T15:44:08Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

The IR spectrum shows that there are 21 visible peaks. From the output file there are in reality 41 vibrations. However for an IR peak to be visible, the vibration must lead to a change in dipole moment.

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

By using a higher level basis set, it is possible to get a better picture of the system and its energy. From the results it may be suggested that the favoured reaction pathway is one with a chair transition state structure because it has a lower activation energy. The reaction can possibly go via a boat transition state under thermodynamic conditions becasue more thermal energy is required to get over the energy barrier. Using this argument, kinetically the chair transition state structure is preferred as less thermal energy is required.<ref name="LIT 3"/>
The sum of the electronic and zero-point energies of the molecules are lower than the sum of the electronic and thermal energies due to the fact that at 0 K there aren't thermal vibrations.

==The Diels-Alder Cycloaddition==

An example of the simplest Diels-Alder cycloaddition can be seen below with a concerted pericyclic mechanism to form the product via a envelope-like transition state.

[[File:Cycloaddition.png]]

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is often strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state. <ref name="LIT 5"/>

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured.<ref name="LIT 6"/> The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å.<ref name="LIT 4"/> The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

The HOMO of the cyclohexadiene interacts with the LUMO of the maleic anhydride, this makes sense as both orbitals are antisymmetric.

The exo product is the one with a lower energy due to the stabilising interactions which are present in the exo product though the endo product has a lower energy of activation.

The endo product HOMO has a higher energy due to the repulsive interaction between the C=O π* orbital and the C=C π*. The exo does not have these repulsive interactions and so is favoured thermodynamically.

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T15:43:07Z

Tf910:

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

The IR spectrum shows that there are 21 visible peaks. From the output file there are in reality 41 vibrations. However for an IR peak to be visible, the vibration must lead to a change in dipole moment.

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

By using a higher level basis set, it is possible to get a better picture of the system and its energy. From the results it may be suggested that the favoured reaction pathway is one with a chair transition state structure because it has a lower activation energy. The reaction can possibly go via a boat transition state under thermodynamic conditions becasue more thermal energy is required to get over the energy barrier. Using this argument, kinetically the chair transition state structure is preferred as less thermal energy is required.<ref name="LIT 3"/>
The sum of the electronic and zero-point energies of the molecules are lower than the sum of the electronic and thermal energies due to the fact that at 0 K there aren't thermal vibrations.

==The Diels-Alder Cycloaddition==

An example of the simplest Diels-Alder cycloaddition can be seen below with a concerted pericyclic mechanism to form the product via a envelope-like transition state.

[[File:Cycloaddition.png]]

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is often strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state. <ref name="LIT 5"/>

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured.<ref name="LIT 6"/> The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

The HOMO of the cyclohexadiene interacts with the LUMO of the maleic anhydride, this makes sense as both orbitals are antisymmetric.

The exo product is the one with a lower energy due to the stabilising interactions which are present in the exo product though the endo product has a lower energy of activation.

The endo product HOMO has a higher energy due to the repulsive interaction between the C=O π* orbital and the C=C π*. The exo does not have these repulsive interactions and so is favoured thermodynamically.

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T15:42:06Z

Tf910:

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

The IR spectrum shows that there are 21 visible peaks. From the output file there are in reality 41 vibrations. However for an IR peak to be visible, the vibration must lead to a change in dipole moment.

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

By using a higher level basis set, it is possible to get a better picture of the system and its energy. From the results it may be suggested that the favoured reaction pathway is one with a chair transition state structure because it has a lower activation energy. The reaction can possibly go via a boat transition state under thermodynamic conditions becasue more thermal energy is required to get over the energy barrier. Using this argument, kinetically the chair transition state structure is preferred as less thermal energy is required.<ref name="LIT 3"/>
The sum of the electronic and zero-point energies of the molecules are lower than the sum of the electronic and thermal energies due to the fact that at 0 K there aren't thermal vibrations.

==The Diels-Alder Cycloaddition==

An example of the simplest Diels-Alder cycloaddition can be seen below with a concerted pericyclic mechanism to form the product via a envelope-like transition state.

[[File:Cycloaddition.png]]

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is often strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured.<ref name="LIT 6"/> The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

The HOMO of the cyclohexadiene interacts with the LUMO of the maleic anhydride, this makes sense as both orbitals are antisymmetric.

The exo product is the one with a lower energy due to the stabilising interactions which are present in the exo product though the endo product has a lower energy of activation.

The endo product HOMO has a higher energy due to the repulsive interaction between the C=O π* orbital and the C=C π*. The exo does not have these repulsive interactions and so is favoured thermodynamically.

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T15:27:44Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

The IR spectrum shows that there are 21 visible peaks. From the output file there are in reality 41 vibrations. However for an IR peak to be visible, the vibration must lead to a change in dipole moment.

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

By using a higher level basis set, it is possible to get a better picture of the system and its energy. From the results it may be suggested that the favoured reaction pathway is one with a chair transition state structure because it has a lower activation energy. The reaction can possibly go via a boat transition state under thermodynamic conditions becasue more thermal energy is required to get over the energy barrier. Using this argument, kinetically the chair transition state structure is preferred as less thermal energy is required.<ref name="LIT 3"/>
The sum of the electronic and zero-point energies of the molecules are lower than the sum of the electronic and thermal energies due to the fact that at 0 K there aren't thermal vibrations.

==The Diels-Alder Cycloaddition==

An example of the simplest Diels-Alder cycloaddition can be seen below with a concerted pericyclic mechanism to form the product via a envelope-like transition state.

[[File:Cycloaddition.png]]

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is often strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

The HOMO of the cyclohexadiene interacts with the LUMO of the maleic anhydride, this makes sense as both orbitals are antisymmetric.

The exo product is the one with a lower energy due to the stabilising interactions which are present in the exo product though the endo product has a lower energy of activation.

The endo product HOMO has a higher energy due to the repulsive interaction between the C=O π* orbital and the C=C π*. The exo does not have these repulsive interactions and so is favoured thermodynamically.

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:40:56Z

Tf910:

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

The IR spectrum shows that there are 21 visible peaks. From the output file there are in reality 41 vibrations. However for an IR peak to be visible, the vibration must lead to a change in dipole moment.

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

By using a higher level basis set, it is possible to get a better picture of the system and its energy. From the results it may be suggested that the favoured reaction pathway is one with a chair transition state structure because it has a lower activation energy. The reaction can possibly go via a boat transition state under thermodynamic conditions becasue more thermal energy is required to get over the energy barrier. Using this argument, kinetically the chair transition state structure is preferred as less thermal energy is required.<ref name="LIT 3"/>
The sum of the electronic and zero-point energies of the molecules are lower than the sum of the electronic and thermal energies due to the fact that at 0 K there aren't thermal vibrations.

==The Diels-Alder Cycloaddition==

An example of the simplest Diels-Alder cycloaddition can be seen below with a concerted pericyclic mechanism to form the product via a envelope-like transition state.

[[File:Cycloaddition.png]]

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is often strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:35:27Z

Tf910: /* The Diels-Alder Cycloaddition */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

The IR spectrum shows that there are 21 visible peaks. From the output file there are in reality 41 vibrations. However for an IR peak to be visible, the vibration must lead to a change in dipole moment.

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

By using a higher level basis set, it is possible to get a better picture of the system and its energy. From the results it may be suggested that the favoured reaction pathway is one with a chair transition state structure because it has a lower activation energy. The reaction can possibly go via a boat transition state under thermodynamic conditions becasue more thermal energy is required to get over the energy barrier. Using this argument, kinetically the chair transition state structure is preferred as less thermal energy is required.
The sum of the electronic and zero-point energies of the molecules are lower than the sum of the electronic and thermal energies due to the fact that at 0 K there aren't thermal vibrations.

==The Diels-Alder Cycloaddition==

An example of the simplest Diels-Alder cycloaddition can be seen below with a concerted pericyclic mechanism to form the product via a envelope-like transition state.

[[File:Cycloaddition.png]]

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is often strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:34:44Z

Tf910: /* The Diels-Alder Cycloaddition */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

The IR spectrum shows that there are 21 visible peaks. From the output file there are in reality 41 vibrations. However for an IR peak to be visible, the vibration must lead to a change in dipole moment.

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

By using a higher level basis set, it is possible to get a better picture of the system and its energy. From the results it may be suggested that the favoured reaction pathway is one with a chair transition state structure because it has a lower activation energy. The reaction can possibly go via a boat transition state under thermodynamic conditions becasue more thermal energy is required to get over the energy barrier. Using this argument, kinetically the chair transition state structure is preferred as less thermal energy is required.
The sum of the electronic and zero-point energies of the molecules are lower than the sum of the electronic and thermal energies due to the fact that at 0 K there aren't thermal vibrations.

==The Diels-Alder Cycloaddition==

An example of the simplest Diels-Alder cycloaddition can be seen below with a concerted pericyclic mechanism to form the product via a envelope-like transition state.

[[File:Cycloaddition.png]]

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

File:Cycloaddition.png

2013-03-15T14:33:05Z

Tf910: uploaded a new version of "File:Cycloaddition.png"

Rep:Mod:tf910

2013-03-15T14:27:00Z

Tf910: /* Energy Summary */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

The IR spectrum shows that there are 21 visible peaks. From the output file there are in reality 41 vibrations. However for an IR peak to be visible, the vibration must lead to a change in dipole moment.

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

By using a higher level basis set, it is possible to get a better picture of the system and its energy. From the results it may be suggested that the favoured reaction pathway is one with a chair transition state structure because it has a lower activation energy. The reaction can possibly go via a boat transition state under thermodynamic conditions becasue more thermal energy is required to get over the energy barrier. Using this argument, kinetically the chair transition state structure is preferred as less thermal energy is required.
The sum of the electronic and zero-point energies of the molecules are lower than the sum of the electronic and thermal energies due to the fact that at 0 K there aren't thermal vibrations.

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:16:22Z

Tf910: /* Ci Anti Conformer */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

The IR spectrum shows that there are 21 visible peaks. From the output file there are in reality 41 vibrations. However for an IR peak to be visible, the vibration must lead to a change in dipole moment.

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:13:05Z

Tf910: /* Ci Anti Conformer */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

Frequency analysis is vital in computational chemistry as it can be used to calculate the minimum structure on the potential energy surface. When the frequencies are positive, it corresponds to the minimum but if one or more of the values are negative it corresponds to the transition state.

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:09:44Z

Tf910:

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"/> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:08:27Z

Tf910:

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value.<ref name="LIT2"> The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="LIT2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:07:12Z

Tf910: /* Ci Anti Conformer */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

This is indicative that when using the higher level basis set, the energy of the molecule is decreased leading to a more stable molecule. The 6-31G(d) basis set also gives an energy value which is closer to the literature value.The results indicate that when using the higher level basis set, it decreases the energy of the molecule which corresponds to a more stable molecule. Using the 6-31G basis set also gives a value of the energy which is closer to the literature value. The values of the bond lengths for C-H and C-C also differ slightly.

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="literature 2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:00:39Z

Tf910:

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="LIT1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="literature 2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T14:00:12Z

Tf910: /* Lowest Energy Conformation */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

Table from Appendix 1:<ref name="LIT1" />

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="Appendix 1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="literature 2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T13:52:54Z

Tf910:

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

==References==

<references>
<ref name="Appendix 1"> https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>

<ref name="literature 2"> G. Schultz, I. Hrgittai, J. Mol. Struct., 1995, 346,63-69</ref>

<ref name="LIT 3"> James H. Cooley and Richard Vaughan Williams; J. Chem. Educ., 1997, 74 (5), p 582</ref>

<ref name="LIT 4"> J. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.</ref>

<ref name="LIT 5"> Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>

<ref name="LIT 6"> Keiji. Morokuma , Weston Thatcher. Borden , David A. Hrovat, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475</ref>
</references>

Rep:Mod:tf910

2013-03-15T13:44:31Z

Tf910: /* Introduction */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

This project looks at the following two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T13:41:16Z

Tf910: /* The Cope Rearrangement */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

The focus on this project is on two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

The Cope rearrangement reaction was named after Arthur Cope who in 1940 discovered that when a 1,5-diene is heated it undergoes a 3,3-sigmatropic rearrangment into an equivalent and more energetically stable regioisomer. The mechanism is an example of a concerted pericyclic reaction. The transition state structures can be either a chair or a boat as seen below:

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T13:08:19Z

Tf910: /* The Cope Rearrangement */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

The focus on this project is on two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

[[File:Cope Rearrangement.png]]

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

File:Cope Rearrangement.png

2013-03-15T13:07:57Z

Tf910:

Rep:Mod:tf910

2013-03-15T13:00:48Z

Tf910: /* Introduction */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

The focus on this project is on two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==The Cope Rearrangement==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:59:09Z

Tf910: /* Introduction */

='''Module 3'''=

==Introduction==

This project involved the analysis and characterisation of the transition states on a Potential Energy Surface for the Cope rearrangement and a Diels-Alder Cycloaddition reaction. This will be done using computational chemistry to examine energy minima of transition states as well as reactants and products and also the effect of orbital interactions on transition state enrgies will be looked at. The real aim is to use these calculations to get a better understanding of these reaction mechanisms and to try to identify why certain transition state structures or reaction products may be favoured over one another.

The program used to carry out these calculations is GaussView 5.0 which enable the modelling of the PES by calculating total energies of the system. GaussView is used to determine the optimal structure of the molecules which participate in reactions.

The focus on this project is on two reactions:
(i) Cope Rearrangement
(ii) Diels-Alder Reaction

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:50:39Z

Tf910: /* Ci Anti Conformer */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:49:59Z

Tf910: /* Ci Anti Conformer */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

{| class="wikitable" border="1" style="text-align: center; margin: 1em auto 1em auto"
|-
| rowspan="1"|
| colspan="4" |'''Equation and Values'''
|-
| Property || Equation || Value
|-
| Sum of electronic and zero-point Energies || E(0 K) = Eelec + ZPE || -234.469202
|-
| Sum of electronic and thermal Energies || E(298.15 K) = E(0 K) + Evib + Erot + Etrans || -234.461855
|-
| Sum of electronic and thermal Enthalpies || H = E (298.15K) + RT || -234.460911
|-
| Sum of electronic and thermal Free Energies || G = H - TS || -234.500777
|}

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:47:46Z

Tf910: /* Hessian Method */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:47:24Z

Tf910: /* Hessian Method */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

The guess transition state structure for the chair transition state was created, two allyl fragments were created and positioned in a chair transition state like structure at a distance of 2.20Å between the terminal carbons.

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:40:32Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

Already knowing that the endo product is kinetically favoured, this can be explianed further by looking at the activation energy values for the endo and exo structure which if correct should show a lower energy of activation for the endo transition state structure. The values can be seen in the table below:

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:36:46Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

The double bond which is formed in the two structures both have the same length at 1.40 Å in the exo and endo transition state. The C=C bond which is converted into a single C-C bond also has length of 1.40 Å in both transition states. This is different from the literature values where a C=C bond is usually 1.34 Å and a C-C is 1.54 Å. Because the product bond lengths are not the same the position of the transition state (early or late) cannot be defined.
When looking at the through space distances both structures have steric hindrance and this is numerically explained by the fact that the through space distances are smaller than the Van der Waals distance of 3.20 Å. The exo transition state through space distance is greater than the endo transition state suggesting that the steric repulsion is lower in the exo transition state structure and consequently more thermodynamically favoured.

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:14:46Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:12:42Z

Tf910: /* Optimal Transition State Structures using a Frozen Coordinate Method */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

The vibration seen above corresponds to the formation of the new sigma bond and the loss of a pi bond. The ethene molecule in the reaction changes hybridisation from sp2 to sp3. This vibration highlights how the ethene interacts with the butadiene and provides insight into how the HOMO and the LUMO orbitals are alligned when they interact to form the bonds. The terminal bond length is greater than is recorded in literature which suggests the C-C bond has not formed - however it is small enough in length to suggest that an orbital interaction is taking place.

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T12:00:58Z

Tf910: /* Reaction of Cyclohexadiene with Maleic Anhydride */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

The scheme for the reaction of cyclohexadiene and maleic anhydride can be seen below showing the two possible products:

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T11:59:44Z

Tf910: /* Reaction of Cyclohexadiene with Maleic Anhydride */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

[[File:Reaction Scheme eve.png]]

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

File:Reaction Scheme eve.png

2013-03-15T11:59:19Z

Tf910:

Rep:Mod:tf910

2013-03-15T10:46:46Z

Tf910: /* Conclusion */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions. The Cope Rearrangement underwent its reaction via a stabilised chair transition state.

The Diels-Alder cycloadditions indicated how orbital symmetry is conserved and how frontier molecular orbital theory can be used to model the transition state structures. The reaction between cis-butadiene and ethene proceeds via an envelope-like transition state explained by the dependence of the frontier orbitals. The reaction between maleic anhydride and cyclohexadiene was seen to form the endo structure under kinetic control. Once again this was explained by the secondary orbital overlap present in the endo structure (but not the exo).

Rep:Mod:tf910

2013-03-15T10:33:57Z

Tf910:

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Conclusion==

The use of computational chemistry in determining and predicting transition state structures has provided additional insight that spectroscopy and other methods cannot model. Because of this, it is possible to predict the likely pathway of chemical reactions by using optimisation and frequency analysis as well as energy calculations to determine key factors that govern the feasibility of reactions such as thermodynamic and kinetic data.

The project involved the computational study of two reactions - the Cope Rearrangement and the Diels-Alder Cycloaddition. Analysis has shown the likely pathways and the structures of the transition states based on the results from the calcualtions.

Rep:Mod:tf910

2013-03-15T10:22:51Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:Exo and Endo Orbital Interactions.png]]

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

File:Exo and Endo Orbital Interactions.png

2013-03-15T10:22:21Z

Tf910:

Rep:Mod:tf910

2013-03-15T10:21:26Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

Rep:Mod:tf910

2013-03-15T10:01:03Z

Tf910:

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

Rep:Mod:tf910

2013-03-15T10:00:46Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:ENDO HOMO.png|300px]] '''HOMO of the EXO transition state'''

[[File:EXO HOMO.png|300px]] '''HOMO of the ENDO transition state'''

==Discussion of Endo and Exo Transition State Structures ==

Rep:Mod:tf910

2013-03-15T09:59:46Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Sum of electronic and thermal energies for the two fragments (a.u.)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the two transition states (a.u.)'''||-612.481358||-612.488746
|-
|''' Activation Energy (a.u.))'''||0.0531||0.04584
|-
|''' Activation Energy (kCal mol-1) (3 d.p.)'''||33.417||28.751
|}

[[File:ENDO HOMO.png|300px]]

[[File:EXO HOMO.png|300px]]

==Discussion of Endo and Exo Transition State Structures ==

Rep:Mod:tf910

2013-03-15T09:54:28Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ Exo and Endo Activation Energies
!Thermodynamic Value !! Exo !! Endo
|-
|'''Total 'Sum of electronic and thermal energies' for the fragments (maleic anhydride + cyclohexadiene)(au)'''||-612.53459||-612.53459
|-
|''' Sum of electronic and thermal energies for the transition states (au)'''||-612.481358||-612.488746
|-
|''' Activation Energy (au))'''||0.0530||0.04580
|-
|''' Activation Energy (kCal mol-1) (3 dp)'''||33.400||28.770
|}

[[File:ENDO HOMO.png|300px]]

[[File:EXO HOMO.png|300px]]

==Discussion of Endo and Exo Transition State Structures ==

Rep:Mod:tf910

2013-03-15T09:52:42Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

[[File:ENDO HOMO.png|300px]]

[[File:EXO HOMO.png|300px]]

==Discussion of Endo and Exo Transition State Structures ==

Rep:Mod:tf910

2013-03-15T09:52:24Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

[[File:ENDO HOMO.png|300px]]

[[File:EXO HOMO.png|350px]]

==Discussion of Endo and Exo Transition State Structures ==

File:EXO HOMO.png

2013-03-15T09:51:52Z

Tf910: uploaded a new version of "File:EXO HOMO.png"

Rep:Mod:tf910

2013-03-15T09:51:15Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

[[File:ENDO HOMO.png|300px]]

==Discussion of Endo and Exo Transition State Structures ==

File:ENDO HOMO.png

2013-03-15T09:50:39Z

Tf910: uploaded a new version of "File:ENDO HOMO.png"

Rep:Mod:tf910

2013-03-15T09:48:58Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

'''Exo and Endo Activation Energies'''

==Discussion of Endo and Exo Transition State Structures ==

Rep:Mod:tf910

2013-03-15T09:48:08Z

Tf910: /* Discussion of Exo and Endo Transition State Structures */

='''Module 3'''=

==Introduction==

==Optimisation and Analysis of 1,5-hexadiene==

===Anti conformation===

The anti conformer of 1,5-hexadiene was drawn using Gaussview and consequently it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24057

[[File:Optimised anti 1,5 hexadiene TF.png|250px]] '''Optimised anti 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised anti 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.69260235 a.u.'''

===Gauche conformation===

As for the anti conformer, the gauche conformer was also drawn using Gaussview and it was optimised using the Hartree-Fock method with a 3-21G basis set. The calculation again was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24061

[[File:Optimised gauche 1,5 hexadiene TF.png|250px|]] '''Optimised gauche 1,5-hexadiene'''

A summary of the data from the optimisation can be seen below:

[[File:Optimised gauche 1,5 hexadiene summary TF.png]]

After symmetrizing, the point group was found to be '''C2'''

Energy: '''-231.68771613 a.u.'''

The Gauche conformer was found to have a higher total energy compared to the anti conformer. The main reason for this is the steric repulsion of the terminal alkene groups which are nearer to each other in the Gauche conformation and so experience greater steric clashing.

=='''Lowest Energy Conformation'''==

{| class="wikitable" border="1" style="text-align:center" align=center
|+ '''Different energies of the 1,5-hexadiene conformers'''
|-
! Conformer !! Structure !! Point Group !! Energy (a.u.)
|-
| Gauche 1 || [[File:Gauche 1 1,5-hexadiene.png|200px]] || C2 || -231.68772
|-
| Gauche 2 || [[File:Gauche 2 1,5-hexadiene.png|200px]] || C2 || -231.69167
|-
| Gauche 3 || [[File:Gauche 3 1,5-hexadiene.png|200px]] || C1 || -231.69266
|-
| Gauche 4 || [[File:Gauche 4 1,5-hexadiene.png|200px]] || C2 || -231.69153
|-
| Gauche 5 || [[File:Gauche 5 1,5-hexadiene.png|200px]] || C1 || -231.68962
|-
| Gauche 6 || [[File:Gauche 6 1,5-hexadiene.png|200px]] || C1 || -231.68916
|-
| Anti 1 || [[File:Anti 1 1,5-hexadiene.png|200px]] || C2 || -231.69260
|-
| Anti 2 || [[File:Anti 2 1,5-hexadiene.png|200px]] || Ci || -231.69254
|-
| Anti 3 || [[File:Anti 3 1,5-hexadiene.png|200px]] || C2h || -231.68907
|-
| Anti 4 || [[File:Anti 4 1,5-hexadiene.png|200px]] || C1 || -231.69097
|-
|}

===Ci Anti Conformer===

'''DFT 3-21G Basis Set'''

The Ci Anti Conformer was optimised using a Hartree Fock method with a 3-21G basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24066

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''3-21G Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 3-21G DFT optimisation can be seen below:

[[File:Optimised 3-21G anti 1,5 hexadiene Ci symmetry summary TF.png]]

'''DFT 6-31G(d) Basis Set'''

The Ci Anti Conformer was further optimised using a DFT method with a 6-31G(d) basis set. The calculation was again run on the HPC server.

D-Space - http://hdl.handle.net/10042/24078

[[File:Optimised 6-31G anti 1,5 hexadiene Ci symmetry molecule TF.png|250px|]] '''6-31G(d) Optimised anti 1,5 hexadiene (Ci symmetry)'''

A summary of the 6-31G(d) DFT optimisation can be seen below:

[[File:Optimised 6-31G anti 1,5 hexadiene Ci summary TF.png]]

'''Frequency Analysis'''

The optimized Ci was consequently used for frequency analysis. The aim of this was to present the minimum critical point on the potential energy surface producing positive real values for the vibrational frequencies. The calculation was run on a HPC server.

D-Space - http://hdl.handle.net/10042/24089

Low frequencies --- -18.8144 -11.7180 -0.0009 -0.0005 -0.0001 1.7514
Low frequencies --- 72.7146 80.1401 120.0114

Zero-point correction= 0.142491 (Hartree/Particle)
Thermal correction to Energy= 0.149847
Thermal correction to Enthalpy= 0.150791
Thermal correction to Gibbs Free Energy= 0.110881
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

'''IR Spectrum of anti 1,5 hexadiene (Ci symmetry):'''

[[File:Anti Ci symmetry 1,5-hexadiene IR Spect..png]]

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

===Hessian Method===

D-Space - http://hdl.handle.net/10042/24127

[[File:Chair TS Guess structure.png|250px]] '''Structure of optimised chair conformation using Hartree Fock and the default basis set 3-21G'''

A summary of the results from the optimisation can be seen below:

[[File:Chair TS Guess summary.png]]

Low frequencies --- -817.9780 -3.5381 -1.0454 -0.0003 0.0001 0.0006
Low frequencies --- 1.1742 209.4810 395.9153
****** 1 imaginary frequencies (negative Signs) ******

Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

The imaginary frequency which is caused by the vibration at -817.98 cm-1 corresponds to what would be expected in the Cope rearrangement.

[[File:Chair TS Movie.gif|250px]]

===Frozen Coordinate Method===

A chair transition state structure (using the optimised allyl fragment) was drawn. This method involved the fixing of the coordinates between the two terminal atom pairs of the allyl fragment which form the TS. They were fixed to approximately 2.20 Å. To do this the redundant coordinates were set to Bond and Freeze Coordinates. Using a Hartree Fock method with a 3-21G basis set the structure was optimised on the HPC server.

D-Space - http://hdl.handle.net/10042/24132

[[File:Frozen coordinate structure.png|250px]] ''' Structure of proposed chair TS optimised by frozen coordinate method '''

The summary of the calculation can be seen below:

[[File:Frozen coordinate summary.png]]

Having carried out the first optimisation, the coordinates were unfrozen and the set to Bond and Derivatives. By doing this the bonds which were previously frozen were optimised by finding the derivative along the PES.

D-Space - http://hdl.handle.net/10042/24138

[[File:Frozen coordinate part 2 structure.png|250px]] ''' Structure of the fully optimised chair TS by frozen coordinate method '''

The summary of the optimisation can be seen below:

[[File:Frozen coordinate part 2 summary.png]]

===Optimisation and Frequency Analysis of Boat===

'''QST2 Method'''

In order to optimise the boat structure an alternative method was used. Two molecules of the previously optimised Ci anti conformer of 1,5-hexadiene were numbered so as one resembled a product and the other a reactant.
The calculation was run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set. The optimisation was unsuccessful due to the fact that the GaussView software is unable to consider the possibility of rotation around the central bonds but only translated the top allyl fragment.

D-Space - http://hdl.handle.net/10042/24138

[[File:Boat TS method 3 part 1 structure.png|250px]] '''Structure of the unsuccessfully optimised boat'''

The summary of the optimisation can be seen below:

[[File:Boat TS method 3 part 1 summary.png]]

To correct this previous error, the reactant and product geometries were modified so that they all resembled the boat transition structure more closely. The central C-C-C-C dihedral angle was changed to 0°. Then the inside C-C-C angles were reduced to 100°. The calculation was again run as a QST2 TS optimisation using a Hartree Fock method and a 3-21G basis set.

D-Space - http://hdl.handle.net/10042/24158

[[File:Boat TS OPT + FREQ 2 structure.png|250px]] '''Structure of the optimised boat conformation'''

The summary of the optimisation can be seen below:

[[File:Boat TS OPT + FREQ 2 summary.png]]

Low frequencies --- -839.9283 -8.0754 -6.3113 -4.0796 0.0003 0.0003
Low frequencies --- 0.0006 155.0909 382.2138
****** 1 imaginary frequencies (negative Signs) ******

[[File:BOAT TS OPT + FREQ 2.gif|250px]] '''Imaginary vibration at -839.93 cm-1

This method was successful to fully optimise the boat TS but as indicated from the first optimisation, there are issues which need to be addressed in order to achieve a successful optimisation. The product and reactant input need to closely resemble the boat TS structure.

==Intrinsic Reaction Coordinate and Analysis of the Chair TS==

When looking at the optimised reactant and product structures as well as the Transition state structures it is not possible to determine whether they connect to form gauche or anti structures of 1,5-hexadiene.

The use of an IRC analysis is to determine the local minimum point to the saddle transition state. In order to achieve this the minimum energy pathway from the transition state to the aforementioned local minimum point is monitored.

During the calculation the molecule's geometry is changed following the steepest section of the reaction energy surface. An IRC was run on the previously optimised chair structure of 1,5-hexadiene to determine the conformation of the structure it forms.

Initially in the IRC, 50 steps were carried out in the forward direction.

D-Space - http://hdl.handle.net/10042/24234

[[File:IRC 1 Movie.gif|250px]] '''50 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 1.png]]

The lowest total Energy = '''-231.69157873 a.u.'''

The IRC using 50 steps did not reach a minimum after the calculation and so it was run again using 100 steps along the reaction coordinate. The resultant structure of lowest energy was hence optimised and then compared to the conformers. It resembled the second gauche conformer (see table above).

D-Space - http://hdl.handle.net/10042/24231

[[File:IRC 2 Movie.gif|250px]] '''100 Step Chair Transition State Iteration Sequence'''

[[File:IRC Graph 2.png|675px]]

The lowest total Energy = '''-231.69156538 a.u.'''

==Activation Energy==

===Chair Optimisation===

The chair was optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24175

[[File:Chair Activation Energy Structure.png|250px]] '''Optimised structure of chair conformer using 6-31G basis set'''

The summary of the optimisation can be seen below:

[[File:Chair Activation Energy summary.png]]

===Chair Frequency Analysis===

The frequency analysis of this chair conformation was done using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D Space - http://hdl.handle.net/10042/24208

The low frequency values have copied from the output file and show that the frequency calculation is finished with one imaginary frequency.

Low frequencies --- -564.9382 -0.0007 0.0006 0.0006 21.3168 26.5951
Low frequencies --- 39.4745 194.3347 268.6930
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.142061 (Hartree/Particle)
Thermal correction to Energy= 0.147980
Thermal correction to Enthalpy= 0.148924
Thermal correction to Gibbs Free Energy= 0.113178
Sum of electronic and zero-point Energies= -234.414924
Sum of electronic and thermal Energies= -234.409005
Sum of electronic and thermal Enthalpies= -234.408061
Sum of electronic and thermal Free Energies= -234.443808

[[File:CHAIR FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -564.9382 cm-1'''

===Boat Optimisation===

The boat conformation was also optimised using the higher 6-31G basis set with a DFT method (B3LYP). The optimisation was run on HPC.

D-Space - http://hdl.handle.net/10042/24179

[[File:Boat Activation Energy Structure.png|250px]] '''Optimised structure of boat conformer using 6-31G basis set'''

A summary of the optimisation can be seen below:

[[File:Boat Activation Energy summary.png]]

===Boat Frequency Analysis===

The frequency analysis of this boat conformation was carried out using the previously optimised chair orientation transition state using DFT method with a 6-31G(d) basis set.

D-Space - http://hdl.handle.net/10042/24214

Low frequencies --- -530.3618 -8.3908 0.0006 0.0008 0.0010 15.4632
Low frequencies --- 17.6137 135.6121 261.7006
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.140751 (Hartree/Particle)
Thermal correction to Energy= 0.147086
Thermal correction to Enthalpy= 0.148030
Thermal correction to Gibbs Free Energy= 0.111341
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

[[File:BOAT FREQ vibration.gif|250px]] '''The Imaginary Frequency vibration at -530.3618 cm-1'''

===Chair and Boat Comparison===

==='''Energy Summary'''===

'''A summary of the total energies in each system after each optimization at a given temperature (Hartrees)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!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="125" 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="125" align="center" | '''Sum of electronic and thermal energies at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466705
| align="center" | -231.461346
| align="center" | -234.556983
| align="center" | -234.414919
| align="center" | -234.408998
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450929
| align="center" | -231.445300
| align="center" | -234.543093
| align="center" | -234.402340
| align="center" | -234.396006
|-
| '''Reactant (''anti2/Ci'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.5322566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}

'''A summary of the activation energies after each optimisation at given temperatures (in kcal/mol)'''

{|class="wikitable" border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''HF/3-21G at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 0 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''B3LYP/6-31G* at 298.15 K (ΔE (kcal/mol)-1)'''
| width="125" align="center" | '''Experimental Values [4](ΔE(kcal/mol)-1)'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.7
| align="center" | 45.3
| align="center" | 34.1
| align="center" | 33.7
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.6
| align="center" | 50.3
| align="center" | 42.0
| align="center" | 37.6
| align="center" | 44.7 ± 2.0
|}

==The Diels-Alder Cycloaddition==

In organic chemistry, the Diels-Alder reaction is a famous example of a cycloaddition reaction. It involves the concerted [4+2] addition of a conjugated diene and an alkene dienophile to form two new carbon-carbon bonds. This reaction is foten strategically used in synthesis because of the fact that it is regio- and stereo-selective. The reaction occurs via a 6-membered transition state which has two possible conformers - exo and endo. In order to allow favourable orbital overlap between the reactants the diene has to be in the cis conformation - this is to maximise the HOMO/LUMO interaction to form two new σ bonds and a π bond. The rate and other characteristics of the reaction can be governed by the use of appropriate electron donating/withdrawing groups.

GaussView will be used to study two Diels-Alder reactions and to characterise the TS and visualise the HOMO and LUMO orbitals.

=== The Addition of Ethylene to Cis-butadiene ===

'''Optimisation of Cis-butadiene'''

Cis-Butadiene was drawn in GaussView and then optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24241

A summary of the optimisation can be seen below:

[[File:Butadiene optimisation summary.png]]

'''Energy (RAM1) =''' 0.04879719

'''Point Group -''' C2v

'''Optimisation of ethene'''

Ethene was then drawn in GaussView and also optimised using the AM1 semi-empirical molecular orbital method. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24242

A summary of the optimisation can be seen below:

[[File:Ethene optimisation summary.png]]

In the case of both of the reactants their optimisations both show an RMS gradient of approximately 0.00001 which is indicative that the optimisations have gone to completion.

'''Energy (RAM1) = ''' 0.02619024

'''Point Group -'''' D2h

The MOs for the HOMO and LUMO of ethene and cis-butadiene can be seen in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Frontier Orbitals of cis-Butadiene and Ethene'''
!Type of MO !! Visualised MO !! Symmetry of MO !!Energy (au)
|-
| cis-Butadiene HOMO|| [[File:Butadiene HOMO TF.png|250px]] ||Anti-symmetric||-0.34381
|-
| cis-Butadiene LUMO|| [[File:Butadiene LUMO TF.png|250px]] ||Symmetric||0.01707
|-
| Ethene HOMO|| [[File:Ethene HOMO.png|250px]] || Symmetric||-0.38777
|-
| Ethene LUMO|| [[File:Ethene LUMO.png|250px]] || Anti-symmetric||0.05284
|}

The below diagram shows the frontier orbitals of cis-butadiene and the MO diagram for ethene:

[[File:MO diagrams ethene and butadiene.png|500px]]

===Optimal Transition State Structures using a Frozen Coordinate Method===

The transition state structure for this Diels-Alder cycloaddition reaction is meant to be envelope-like. The structure was optimised using the semi empirical AM1 system using the frozen coordinate method which was used previously with the terminal carbons set at a distance of 2.20 Å from each other.

D-Space - http://hdl.handle.net/10042/24256

[[File:Froz. Coord. Summary.png]]

'''Frequency Analysis'''

Frequency analysis was also conducted using the same method and basis set.

D-Space - http://hdl.handle.net/10042/24258

A summary of the frequency analysis can be seen below:

[[File:Froz. Coord. Freq Summary.png]]

As can be seen from the table above there is an imaginary frequency present at -977.89 cm-1. This indicates the presence of a transition state.

[[File:Imaginary Vib. Frozen Coord..gif|250px]] '''Vibration corresponding to -977.89 cm-1 which indicates the transition state structure'''

The low frequency values have been presented from the output log file and show that the frequency calculation is complete:

Low frequencies --- -977.8947 -79.0965 -60.7487 -0.0418 -0.0022 0.0091
Low frequencies --- 9.0873 140.4152 237.8229
****** 1 imaginary frequencies (negative Signs) ******

Zero-point correction= 0.141403 (Hartree/Particle)
Thermal correction to Energy= 0.147729
Thermal correction to Enthalpy= 0.148674
Thermal correction to Gibbs Free Energy= 0.111992
Sum of electronic and zero-point Energies= 0.254930
Sum of electronic and thermal Energies= 0.261257
Sum of electronic and thermal Enthalpies= 0.262201
Sum of electronic and thermal Free Energies= 0.225519

===Comparison of Transition State Structures===

When the bond lengths are compared with the respective calculation methods and the literature values of actual bond lengths it gives an indication on the nature of the transition state.

Looking at the methods used the DFT (6-31G(d)) basis set gave a much higher value for the terminal C-C bonds which is closer to the literature value than the Semi-Empirical (AM1) method.

Because of the fact that the DFT terminal bond length is longer it is suggestive that the transition state is earlier with respect to the semi-empirical structure.

In the transition state the double bonds of the ethene and the cis-butadiene fragments have longer bond lengths than the would be typically expected for C=C though it is not as long as the C-C single bonds as is predicted.

===MO Analysis of Envelope Transition State===

[[File:HOMO.png|350px]] '''The HOMO Molecular Orbital (Energy = -0.32394 a.u.)'''

[[File:LUMO TF.png|350px]] '''The LUMO Molecular Orbital (Energy = -0.02316 a.u.)'''

The HOMO molecular orbital is symmetrical and weakly bonding and this can be justified from the number of nodes present. From this we know that the fragment orbitals which overlap are both antisymmetric .

The LUMO molecular orbital is antisymmetric with respect to the symmetry plane and has a higher number of nodes - for this reason it can be seen to be antibonding.

==Reaction of Cyclohexadiene with Maleic Anhydride==

When looking at the reaction between cyclohexadiene and maleic anhydride, mechanisms can be feasibly drawn to show the formation of the endo or exo product. When performed in the lab the endo product is found to be the kinetically favoured product whereas the exo product is thermodynamically favoured. The kinetic preference to the endo product can be explained by orbital interactions in the transition state which can be examined using computational calculations done on GaussView.

===Optimising Maleic Anhydride and Cyclohexadiene Fragments===

Prior to the construction of the guess endo and exo transition states, both of the reactant fragments were optimised using the DFT method with a 6-31G(d) basis set. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24315

[[File:Maleic Anhydride Opt Structure.png|250px]] '''Structure of optimised maleic anhydride using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Maleic Anhydride Opt Summary.png]]

The cyclohexadiene was optimised in the same way as the maleic anhydride fragment, that is to say using the DFT method with a 6-31G(d) basis set. Again the calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24316

[[File:Cyclohexadiene summary.png|250px]] '''Structure of optimised cyclohexadiene using 6-31G(d) basis set'''

A summary of the optimisation data can be seen below:

[[File:Cyclohexadiene structure.png]]

The HOMOs and LUMOs for both fragments have been visualised in GaussView and are presented in the table below:

{| class="wikitable" border="1" align="center" style="text-align:center"
|+ '''The Molecular Orbitals of maleic anydride and cyclohexadiene'''
!Type of MO !! Visualised MO !! Symmetry !! Energy (a.u.)
|-
| Maleic Anhydride HOMO||[[File:Maleic Anhydride HOMO.png|250px]]||Symmetric||-0.29928
|-
| Maleic Anhydride LUMO||[[File:Maleic Anhydride LUMO.png|250px]]||Anti-symmetric||-0.11712
|-
| Cyclohexadiene HOMO||[[File:Cyclohexadiene HOMO.png|250px]]||Anti-symmetric||-0.20551
|-
| Cyclohexadiene LUMO||[[File:Cyclohexadiene LUMO.png|250px]]||Symmetric||-0.01710
|}

If you analyse the molecular orbitals of both fragements you can see that the HOMO of maleic anhydride is strongly bond - largely due to the favourable bonding interactions which are seen on the ring and the oxygens. On the other hand the LUMO consists mainly of antibonding interactions and this is highlighted by the number of nodes which are present on the alkene and carbonyl bonds.

Looking at the cyclohexadiene fragment, the HOMO is symmetrical and has a node in the centre. Antibonding interactions are evident although there are also some bonding interactions which would imply that the MO is weakly bonding. Looking at the LUMO it is clearly symmetrical and antibonding interactions dominate highlighted by the number of nodes.

Comparison of the energies of the respective HOMO and LUMO of maleic anhydride show there to be a large gap in energy compared to cyclohexadiene. Therefore maleic anhydride is able to accept electron density from the HOMO of cyclohexadiene. Since both orbitals are antisymmetric the interaction is allowed and favourable.

==Analysis of Endo and Exo Transition States==

===EXO===

Taking the optimised fragments of maleic anhydride and cyclohexadiene, an exo transition state was drawn on GaussView. The terminal carbon atoms were frozen as done previously at 2.10 Å. The calculation was run on the HPC server.

D-Space - http://hdl.handle.net/10042/24323

A summary of the data from the calculation can be seen below:

[[File:Exo opt summary.png]]

'''Exo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24321

Zero-point correction= 0.181203 (Hartree/Particle)
Thermal correction to Energy= 0.191644
Thermal correction to Enthalpy= 0.192588
Thermal correction to Gibbs Free Energy= 0.144725
Sum of electronic and zero-point Energies= -612.495476
Sum of electronic and thermal Energies= -612.485035
Sum of electronic and thermal Enthalpies= -612.484091
Sum of electronic and thermal Free Energies= -612.531953

Low frequencies --- -466.4669 -31.5915 -24.1975 -0.0005 -0.0001 0.0005
Low frequencies --- 2.8268 46.8664 106.1689
****** 1 imaginary frequencies (negative Signs) ******

[[File:Exo Freq Vibration.gif|250px]] '''Imaginary Frequency vibration at -466.47 cm-1'''

This vibration relates to the concerted formation of two sigma bonds

===ENDO===

The endo transition state was drawn on GaussView using the optimised fragments of maleic anhydride and cyclohexadiene. The same procedure was carried out as for the exo transition state.

D-Space - http://hdl.handle.net/10042/24325

A summary of the data from the calculation can be seen below:

[[File:Endo opt summary.png]]

'''Endo Frequency Analysis'''

D-Space - http://hdl.handle.net/10042/24327

Zero-point correction= 0.180921 (Hartree/Particle)
Thermal correction to Energy= 0.190736
Thermal correction to Enthalpy= 0.191680
Thermal correction to Gibbs Free Energy= 0.145465
Sum of electronic and zero-point Energies= -612.487786
Sum of electronic and thermal Energies= -612.477970
Sum of electronic and thermal Enthalpies= -612.477026
Sum of electronic and thermal Free Energies= -612.523242

Low frequencies --- -480.7068 -52.3975 -41.9664 -30.8204 0.0007 0.0008
Low frequencies --- 0.0011 26.5110 78.9781
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo Freq Vibration.gif]] '''Imaginary Frequency vibration at -480.71 cm-1'''

==Discussion of Exo and Endo Transition State Structures ==

It has been generally mentioned that the endo product is kinetically favoured and the exo product is thermodynamically favoured and that it can be explained by the orbital interactions which produce a stabilising effect. From the calculations done on the optimised structures of the two products and the determination of the activation energies it is consequently possible to explain the characteristics in more detail.

{| class="wikitable" border="1" align=centre style="text-align:center"
|+ ''' A Comparison of Transition State Structures'''
!Parameter (Å) !! Exo !! Endo
|-
|'''C-C Inter-fragment Bond Length'''||2.29||2.27
|-
|'''Bond Length in Maleic Anhydride '''||1.48||1.48
|-
|'''Bond Length in cyclohexadiene'''||1.53||1.54
|-
|'''New C-C Bond Length'''||1.40||1.39
|-
|''' New C=C Bond Length '''||1.40||1.40
|-
|'''Through Space Distance ''' ||2.96||2.87
|}

The mechanism for the cycloaddition requires the movement of electrons which occupy π orbitals into σ orbitals while forming two new σ bonds and getting rid of two π bonds while a new π bond is also formed on the diene. The maleic anhydride alkene bond is also converted into a single C-C bond.

'''Bond Lengths'''

==Discussion of Endo and Exo Transition State Structures ==