ChemWiki - User contributions [en]

ILabber

2012-03-30T14:15:17Z

Jw1707:

= iLabber Trial =

== Launch ==
Dear all,

You will have all received a login password for iLabber.

I queried the lack of any pre-built templates with Accelrys, and received this reply "Dear Prof. Rzepa, I checked with my colleagues from support. There are no default templates in iLabber, this allows flexibility to create own templates from the sections offered. However you can ask other coordinators from the iLabber pilot to send you a PDF of a template to see what sections they are using for Computational Chemistry experiments. If you need further information please do not hesitate to contact me." I have to admit that I have not yet been "trained" in the art of creating a project template, and Richard Whitby tells me that "Given the functionality I am not sure how important pre-defiend templates will be(though we are trying to produce an excel based one to accelerate entry of safety data)".

I would like everyone on this pilot to look through the features of iLabber, and consider how they might use the functionality for their own lab work. If you find the process difficult, record that as well. It might be a good idea if we all met in person to discuss the first few weeks experience of the system. Already I find the Help pages rather minimalist. Indeed, perhaps having an expert actually demonstrate the system might be a help.

There are many ways in which we could keep a local account of experiences, hints, etc. We could start by repeating how we documented the earlier MnovaDB trial, by going to https://wiki.ch.ic.ac.uk/wiki/index.php?title=ILabber and depositing your thoughts there. I have already been asked to complete a survey of the national project, at https://www.isurvey.soton.ac.uk/4882/36830/8Q9F6A/Imperial+College+London (this survey is user specific - use the link emailed to you individually) to document how we found the start of the project

and there is also an invitation to join a Google groups forum at http://groups.google.com/group/ilabber-uk-academic-pilot/sub?s=1ednLBQAAADwPLnPNldBKZy0eNokB47rTs88g-WnFbb4C853MSmguA&hl=en-GB (which may be email specific). These requests could easily become intrusive, and so we should strive to keep them to a minimum. I hope however that this email is not quite in that category!--[[User:Rzepa|Rzepa]] 17:22, 23 March 2012 (UTC)

----

I've had 2 attempts at using iLabber. One failed at the first step with an error message that my office PC software is not compatible with iLabber " iLabber does not run on this browser/computer combination"

My first attempt on my Mac Airbook was more successful in logging on and creating a new project and experiment. The snag here was that iLabber can't see that I have ChemDraw installed. I have the option to install MarvinDraw with the threat that I will need to upgrade to iLabber Premium in 2 weeks time. With a four day college closure during the next 2 weeks, this could be a short trial unless we can be upgraded.

Andy

___

Using the ilabber seems generally quite straight-forwards. You basically insert text boxes, image boxes and chemical reaction boxes relavent to your experiment.
I tried using the Windows Client but it seems to run quite slowly and is giving me trouble with ChemDraw.
Also shame there isn't a better way to insert NMR spectra.

Yoni

Rep:Mod:Jw1707c

2010-02-22T18:30:06Z

Jw1707: /* References */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:ENDOHOMO.jpg|thumb|200px|'''''The HOMO of the Endo isomer, note there is no node between the orbitals on the alkene and thos on the central Oxygen''''']][[Image:EXOHOMO.jpg|thumb|200px|'''''The HOMO of the Exo isomer, note the node on the central Oxygen and the adjacent orbitals''''']]
The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -612.68339704 hartree and that of the exo as -612.67931095. Which has an energy difference of 10.73 kJ/mol. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

In the endo isomer the bond length of the bonds being formed was calculated as 2.27Å whereas this bond length was 2.29Å in the exo structure.
The distance between the carbon on the O=C-O-C=O fragment and the C on the opposite CH on the other fragment was 2.991Å for the endo and 3.03Å for the equivalent C to CH2 in the exo. This seems to imply that the maleic anhydride fragment is being pulled in, in the endo isomer but being pushed away in the exo isomer.
The reason for these differences in bond length can be explained by a closer look at HOMO of each isomer and the phenomenon of secondary orbital overlap<ref name="ja9825332"> Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet ''J. Org. Chem.'', '''1987''', 52 (8), p 1469{{DOI|10.1021/jo00384a016}}</ref> . In the endo isomer there is no node between the orbitals on the central oxygen and and the orbitals on the alkenes of the other fragment, the molecule tries to maximise this overlap by bringing the two fragments nearer but on the other hand the steric repulsion between the two fragments is increased by bringing them nearer so an equilibrium value is found, however the exo fragment has a node between the oxygen orbitals and opposing fragment and therefore the molecule doesn't want to pull the fragments any closer and hence the difference in the carbon carbon distances.

==References==
<references />

Rep:Mod:Jw1707c

2010-02-22T18:23:50Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

Rep:Mod:Jw1707c

2010-02-22T18:22:46Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
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====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -612.68339704 hartree and that of the exo as -612.67931095. Which has an energy difference of 10.73 kJ/mol. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

[[Image:ENDOHOMO.jpg|thumb|250px|'''''The HOMO of the Endo isomer, note there is no node between the orbitals on the alkene and thos on the central Oxygen''''']][[Image:EXOHOMO.jpg|thumb|250px|'''''The HOMO of the Exo isomer, note the node on the central Oxygen and the adjacent orbitals''''']]
In the endo isomer the bond length of the bonds being formed was calculated as 2.27Å whereas this bond length was 2.29Å in the exo structure.
The distance between the carbon on the O=C-O-C=O fragment and the C on the opposite CH on the other fragment was 2.991Å for the endo and 3.03Å for the equivalent C to CH2 in the exo. This seems to imply that the maleic anhydride fragment is being pulled in, in the endo isomer but being pushed away in the exo isomer.
The reason for these differences in bond length can be explained by a closer look at HOMO of each isomer and the phenomenon of secondary orbital overlap<ref name="ja9825332"> Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet ''J. Org. Chem.'', '''1987''', 52 (8), p 1469{{DOI|10.1021/jo00384a016}}</ref> . In the endo isomer there is no node between the orbitals on the central oxygen and and the orbitals on the alkenes of the other fragment, the molecule tries to maximise this overlap by bringing the two fragments nearer but on the other hand the steric repulsion between the two fragments is increased by bringing them nearer so an equilibrium value is found, however the exo fragment has a node between the oxygen orbitals and opposing fragment and therefore the molecule doesn't want to pull the fragments any closer and hence the difference in the carbon carbon distances.

===References===
<references />

Rep:Mod:Jw1707c

2010-02-22T18:18:49Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
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====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -612.68339704 hartree and that of the exo as -612.67931095. Which has an energy difference of 10.73 kJ/mol. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

[[Image:ENDOHOMO.jpg|thumb|250px|'''''The HOMO of the Endo isomer, note there is no node between the orbitals on the alkene and thos on the central Oxygen''''']][[Image:EXOHOMO.jpg|thumb|250px|'''''The HOMO of the Exo isomer, note the node on the central Oxygen and the adjacent orbitals''''']]
In the endo isomer the bond length of the bonds being formed was calculated as 2.27Å whereas this bond length was 2.29Å in the exo structure.
The distance between the carbon on the O=C-O-C=O fragment and the C on the opposite CH on the other fragment was 2.991Å for the endo and 3.03Å for the equivalent C to CH2 in the exo. This seems to imply that the maleic anhydride fragment is being pulled in, in the endo isomer but being pushed away in the exo isomer.
The reason for these differences in bond length can be explained by a closer look at HOMO of each isomer and the phenomenon of secondary orbital overlap. In the endo isomer there is no node between the orbitals on the central oxygen and and the orbitals on the alkenes of the other fragment, the molecule tries to maximise this overlap by bringing the two fragments nearer but on the other hand the steric repulsion between the two fragments is increased by bringing them nearer so an equilibrium value is found, however the exo fragment has a node between the oxygen orbitals and opposing fragment and therefore the molecule doesn't want to pull the fragments any closer and hence the difference in the carbon carbon distances.

Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet

J. Org. Chem., 1987, 52 (8), pp 1469–1474

DOI: 10.1021/jo00384a016

Rep:Mod:Jw1707c

2010-02-22T18:08:45Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -612.68339704 hartree and that of the exo as -612.67931095. Which has an energy difference of 10.73 kJ/mol. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

[[Image:ENDOHOMO.jpg|thumb|250px| '''''The HOMO of the Endo isomer, note there is no node between the orbitals on the alkene and thos on the central Oxygen''''']][[Image:EXOHOMO.jpg|thumb|250px| '''''The HOMO of the Exo isomer, note the node on the central Oxygen and the adjacent orbitals''''']]
In the endo isomer the bond length of the bonds being formed was calculated as 2.27Å whereas this bond length was 2.29Å in the exo structure.
The distance between the Carbon on the O=C-O-C=O fragment and the C on the opposite CH on the other fragment was 2.991Å for the endo and 3.03Å for the equivalent C to CH2 in the exo.
The reason for these differences in bond length can be explained by a closer look at HOMO of each isomer. In the endo isomer there is no node between the

Rep:Mod:Jw1707c

2010-02-22T18:05:06Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -612.68339704 hartree and that of the exo as -612.67931095. Which has an energy difference of 10.73 kJ/mol. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

In the endo isomer the bond length of the bonds being formed was calculated as 2.27Å whereas this bond length was 2.29Å in the exo structure.
The distance between the Carbon on the O=C-O-C=O fragment and the C on the opposite CH2 on the other fragment was 3.94Å for the endo and 3.88Å for the equivalent in the exo.
The reason for these differences in bond length can be explained by a closer look at HOMO of each isomer.
[[Image:ENDOHOMO.jpg|thumb|250px| '''''The HOMO of the Endo isomer, note there is no node between the orbitals on the alkene and thos on the central Oxygen''''']][[Image:EXOHOMO.jpg|thumb|250px| '''''The HOMO of the Exo isomer, note the node on the central Oxygen and the adjacent orbitals''''']]

File:ENDOHOMO.jpg

2010-02-22T18:00:23Z

Jw1707:

File:EXOHOMO.jpg

2010-02-22T18:00:08Z

Jw1707:

Rep:Mod:Jw1707c

2010-02-22T17:56:14Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -612.68339704 hartree and that of the exo as -612.67931095. Which has an energy difference of 10.73 kJ/mol. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

In the endo isomer the bond length of the bonds being formed was calculated as 2.27Å whereas this bond length was 2.29Å in the exo structure.
The distance between the Carbon on the O=C-O-C=O fragment and the C on the opposite CH2 on the other fragment was 3.94Å for the endo and 3.88Å for the equivalent in the exo.
The reason for these differences in bond length can be explained by a closer look at HOMO of each isomer.

Rep:Mod:Jw1707c

2010-02-22T17:52:52Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -612.68339704 hartree and that of the exo as -612.67931095. Which has an energy difference of 10.73 kJ/mol. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

In the endo isomer the bond length of the bonds being formed was calculated as 2.27Å whereas this bond length was 2.29Å in the exo structure.
The distance between the Carbon on the O=C-O-C=O fragment and the C on the opposite CH2 on the other fragment was 3.94Å for the endo and 3.88Å for the equivalent in the exo.
The reason for this is that the

Rep:Mod:Jw1707c

2010-02-22T17:50:22Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -612.68339704 hartree and that of the exo as -612.67931095. Which has an energy difference of 10.73 KJ/mol. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

In the endo isomer the bond length of the bonds being formed was calculated as 2.162Å whereas this bond length was 2.170Å in the exo structure.
The distance between the Carbon on the O=C-O-C=O fragment and the C on the opposite CH2 on the other fragment was 3.897Å for the endo and 3.781Å for the equivalent in the exo.
The reason for this is that the

Rep:Mod:Jw1707c

2010-02-22T17:33:23Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
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</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -0.05150480 hartree and that of the exo as -0.05041985. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

In the endo isomer the bond length of the bonds being formed was calculated as 2.162Å whereas this bond length was 2.170Å in the exo structure.
The distance between the Carbon on the O=C-O-C=O fragment and the C on the opposite CH2 on the other fragment was 3.897Å for the endo and 3.781Å for the equivalent in the exo.
The reason for this is that the

Rep:Mod:Jw1707c

2010-02-22T17:22:28Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -0.05150480 hartree and that of the exo as -0.05041985. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

In the endo isomer the bond length of the bonds being formed was calculated as 2.162Å whereas this bond length was 2.170Å in the exo structure.

Rep:Mod:Jw1707c

2010-02-22T17:15:24Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -0.05150480 hartree and that of the exo as -0.05041985. Showing the endo to be lower in energy, since this is a kinetically controlled reaction, this means that the endo should be the major product which it is experimentally.

Rep:Mod:Jw1707c

2010-02-22T17:03:55Z

Jw1707: /* Diels Alder */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.
For this section the transition states were first optimised using the semi empirical AM1 molecular orbital basis set which was fairly fast for these bigger molecules but generally a low basis set. Once the transition states had been optimised they were then re-optimised at the higher B3LYP 6-31G* basis set which gives more accurate results.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -0.05150480 hartree and that of the exo as -0.05041985. Showing the endo to be significantly lower in Energy.

Rep:Mod:Jw1707c

2010-02-22T16:46:57Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -0.05150480 hartree and that of the exo as -0.05041985. Showing the endo to be significantly lower in Energy.

Rep:Mod:Jw1707c

2010-02-22T16:44:23Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.
A quick look at the output file gives the endo energy as -0.05150480 hartree

Rep:Mod:Jw1707c

2010-02-22T16:41:30Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

The difference between the endo and exo forms is that in the endo case the three oxygen atoms of the maleic anhydride are tucked in under the alkene groups in the cyclodiene whereas in the exo case they are point out.
It is clearly the electrostatic and steric interactions between the alkenes and oxygens which will determine which is more stable.

Rep:Mod:Jw1707c

2010-02-22T16:38:37Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following endo and exo products respectively:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>EndoTS631.mol</uploadedFileContents>
</jmolApplet><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ExoTS631.mol</uploadedFileContents>
</jmolApplet></jmol>

Rep:Mod:Jw1707c

2010-02-22T16:36:26Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|left|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

The transition structures were computed as above using the Berny Force field Transition State calculation, giving the following products:

File:ExoTS631.mol

2010-02-22T16:36:14Z

Jw1707:

File:EndoTS631.mol

2010-02-22T16:35:57Z

Jw1707:

Rep:Mod:Jw1707c

2010-02-22T16:33:49Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

[[Image:Exoendo.JPG|thumb|right|Cyclohexa-1,3-diene and maleic anhydride to give the exo and endo isomers]]

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

File:Exoendo.JPG

2010-02-22T16:31:51Z

Jw1707:

Rep:Mod:Jw1707c

2010-02-22T16:04:59Z

Jw1707: /* Cyclohexa-1,3-diene and maleic anhydride diels alder reaction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

The previous reaction was between to symmetric molecules, we will now calculate the transition states for a diels alder reaction which can take one of two stereoisomers, a comparison of the properties of the two stereoisomers will give us more insight into the nature of the reaction and allow us to predict which stereoisomer will be formed in a kinetic reaction.

Rep:Mod:Jw1707c

2010-02-22T16:01:06Z

Jw1707: /* Transition State Optimisation */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Cyclohexa-1,3-diene and maleic anhydride diels alder reaction====

Rep:Mod:Jw1707c

2010-02-22T15:59:32Z

Jw1707: /* Diels Alder */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

==Diels Alder==

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

Rep:Mod:Jw1707c

2010-02-22T15:59:15Z

Jw1707: /* Introduction */

==Introduction==

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

Rep:Mod:Jw1707c

2010-02-22T15:59:05Z

Jw1707: /* Cope rearrangement tutorial */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

==Cope rearrangement tutorial==

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

Rep:Mod:Jw1707c

2010-02-22T15:58:27Z

Jw1707: /* Transition State Optimisation */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen in the images on the side,

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once. This clearly demonstrates that the diels alder reaction is concerted and not done in steps. A look at the lowest couple of positive frequencies show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

Rep:Mod:Jw1707c

2010-02-22T15:55:30Z

Jw1707: /* Transition State Optimisation */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once, this is as opposed to the lowest couple of positive frequencies which show an interaction between the butadiene and the ethene but asynchronously as seen here:
<jmol>
<jmolAppletButton>
<title>Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 64;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>
<jmol>
<jmolAppletButton>
<title>Second Lowest Positive Frequency</title><color>white</color><size>500</size>
<script>zoom 150;frame 65;vectors 5;vectors scale 1;color vectors red;vibration 4;</script>
<uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolAppletButton>
</jmol>

Rep:Mod:Jw1707c

2010-02-22T15:49:04Z

Jw1707: /* Transition State Optimisation */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once, this is as opposed to the lowest couple of positive frequencies which show an interaction between the butadiene and the ethene but asynchronously as seen here:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>zoom 100;frame 64;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>zoom 100;frame 65;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Rep:Mod:Jw1707c

2010-02-22T15:46:04Z

Jw1707: /* Transition State Optimisation */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum on the potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The reaction can clearly be seen to be synchronous, i.e. both bonds are being formed at once, this is as opposed to the lowest positive frequency which shows an interaction between the butadiene and the ethene but asynchronously see here:
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 64;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Rep:Mod:Jw1707c

2010-02-22T15:40:46Z

Jw1707: /* Transition State Optimisation */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum onthe potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 63;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>DIELS_TS_OPTFREQ9.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

File:DIELS TS OPTFREQ9.LOG

2010-02-22T15:38:56Z

Jw1707:

Rep:Mod:Jw1707c

2010-02-22T15:38:14Z

Jw1707: /* Transition State Optimisation */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

A look at the vibrational frequecies, shows one negative/ imaginary frequency which confirms that this is indeed a maximum onthe potential energy surface. A look at this vibration also tells us a bit about the reaction:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

Rep:Mod:Jw1707c

2010-02-22T15:36:34Z

Jw1707: /* Cis Butadiene and Ethene */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

=====Optimisation of Fragments=====
Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

=====Transition State Optimisation=====
Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

Rep:Mod:Jw1707c

2010-02-22T15:32:48Z

Jw1707: /* Cis Butadiene and Ethene */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't a proper covalent bond and yet the van-der-waals radius of a carbon atom is 1.70Å so the bond length of 2.12Å is clearly a lot less than the 3.40Å we would expect of there was no bonding whatsoever, instead we have some intermediate stage if bonding which is what one would expect at the transition state.

Rep:Mod:Jw1707c

2010-02-22T15:28:18Z

Jw1707: /* Cis Butadiene and Ethene */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares to typical σ C-C bond lengths of 1.53Å or 1.46Å for sp3 and sp2 C-C bonds respectively (from the CRC handbook of chemistry and Physics 90th Edition)showing that the bond clearly isn't yet a full C-C bond...

Rep:Mod:Jw1707c

2010-02-22T15:10:32Z

Jw1707: /* Cis Butadiene and Ethene */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

The calculated bond length of the C-C bond being formed in the transition state structure is 2.119Å, this compares the

Rep:Mod:Jw1707c

2010-02-22T15:06:08Z

Jw1707: /* Cis Butadiene and Ethene */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

Rep:Mod:Jw1707c

2010-02-22T15:04:55Z

Jw1707: /* Cis Butadiene and Ethene */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|none|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|none|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure. Seen here:

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Diels_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

File:Diels ts opt.mol

2010-02-22T15:04:32Z

Jw1707:

Rep:Mod:Jw1707c

2010-02-22T15:01:30Z

Jw1707: /* Cis Butadiene and Ethene */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|none|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|none|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure.

The molecular orbitals of this transition state structure was visualised, of particular importance is the HOMO and LUMO orbitals seen below:

[[Image:Diels_ts_HOMO.jpg|thumb|200px|Diels Alder Transition state HOMO]][[Image:Diels_ts_LUMO.jpg|thumb|200px|Diels Alder Transition State LUMO]]

As can be seen, with respect to the same vertical plane, the transition state HOMO is antisymmetric while the LUMO is symmteric.
A closer look at the transition state HOMO shows that it is essentially made up of an overlap between the butadiene HOMO and the ethene LUMO, which both had antisymmetric symmetry as stated above. In addition there is a large amount of electron density between the ethene fragment and the butadiene fragment indicating where the bond is forming.

Rep:Mod:Jw1707c

2010-02-22T14:55:08Z

Jw1707: /* Cis Butadiene and Ethene */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|none|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|none|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure.
The molecular orbitals of this transition state structure was visualised,
[[Image:Diels_ts_HOMO.jpg|thumb|none|200px|Diels Alder Transition state HOMO]]
[[Image:Diels_ts_LUMO.jpg|thumb|none|200px|Diels Alder Transition State LUMO]]

File:Diels ts LUMO.jpg

2010-02-22T14:53:57Z

Jw1707:

Rep:Mod:Jw1707c

2010-02-22T14:49:22Z

Jw1707: /* Cis Butadiene and Ethene */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.

[[Image:CisbutadieneLUMO.jpg|thumb|none|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|none|200px|Cis butadiene HOMO]]

With respect to a plane of symmetry dissecting the molecule vertically, the HOMO can be seen to be antisymmetric whilst the LUMO is symmetric.

Whilst for the ethene molecule, the opposite is the case. This is very significant as a reaction will only occur between two molecular orbitals of the same symmetry.

Putting the two optimised structures in the same window and optimising the approximate angles and bond lengths manually, before doing a Berny Transition state structure optimisation, yielded eventually a transition state structure.
The molecular orbitals of this transition state structure was visualised, [[Image:Diels_ts_HOMO.jpg|thumb|none|200px|Cis butadiene HOMO]]

File:Diels ts HOMO.jpg

2010-02-22T14:47:34Z

Jw1707:

Rep:Mod:Jw1707c

2010-02-22T14:38:50Z

Jw1707: /* Diels Alder */

===Introduction===

This module will focus on using theoretical and computational methods to optimise and calculate properties of the transition state in reactions.
The methods used here differ from those in the previous units as we are no longer seeking the minimal energy to find the optimised conformation.
Two different methods were used as described below:

===Cope rearrangement tutorial===

====Optimisation of starting product====

Initially the starting product of a simple cope reaction was optimised:

[[Image:pic1.jpg|right|thumb|Cope rearrangement]]

The 1,5 hexadiene was built in the Gaussview programme and the dihedral angle set to give an anti configuration. This was optimised using the relatively low basis set; HF/3-21G.

Even this relatively simple molecule can have many different configurations as each C-C bond can rotate to give a different relative conformation. These different configurations will obviously have different symmetries and different energies based on several factors

The first optimisation gave the anti2 conformation, the molecule was rearranged manually by adjusting dihedral angles and several different conformers were optimised the key ones are summarised in the following table:

<center>
{| class="wikitable" border="1"
|+ '''''Conformations of 1,5 hexadiene'''''
! !!Conformer Name!! Energy (a.u.)!! Symmetry point group
|-
| [[Image:JWAnti1.jpg|200px]]||Anti1 || -231.69260236||C2
|-
| [[Image:JWAnti2.jpg|200px]]||Anti2 || -231.69253528||Ci
|-
| [[Image:JWGauche1.jpg|200px]]||Gauche1 || -231.68771616 a.u.||C2
|-
| [[Image:JWAnti4.jpg|200px]]||Anti4|| -231.69097057 a.u.|| C1
|-
| [[Image:JWGauche3.jpg|200px]]||Gauche 3 ||-231.69266122 a.u. ||C1
|}
</center>

[[Image:JWGauche3MO.jpg|right|200px]]
One would initially expect the lowest energy conformation to be an anti conformation, such that all the carbons are anti periplanar to eachother minimising steric repulsions yet the Gauche3 is the lowest energy conformation (although marginally) The reason for this is that the energy is not just dependent on steric factors. There is also hyperconjaction effects and Molecular Orbital overlap effects, as can be seen in the following image. There is a stabilising overlap effect between the pi clouds over the two alkene bonds, this isn't present in the anti configurations as the alkene groups are seperated away from eachother by the antiperiplanar bonds.

=====Further optimisation of anti conformation=====
The Anti2 conformation was used as the starting product in our theoretical cope rearrangement. So it was further optimised with a higher B3LYp-631-G(d) basis set.
The resulting structure had an energy of -234.61170277a.u. which is a significant drop in energy compared to the previous optimisation. The actual change in geometry was marginal with the only noticeable difference being a change in bond angle between the H-C-H on the central carbons from 107.7° to 106.7°

A vibrational calculation was made at the same basis set to the frequency values, this confirmed that the geometry was at a minimum by providing all positive values as well as giving us frequency information.

The following thermo-chemistry results were produced:
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 = -234.500821
Of particular importance is the first and second values which tell us the potential energy at 0°K and 298.15°k respectively.

====Chair and Boat Conformation====

Now that the starting product has been optimised, the next stage is to optimise the transition structure.
There are two possible transition structures known in the literature, these being the boat and the chair conformation.

=====Chair C<sub>2h</sub> transition state=====
======TS berny method======
Initially an allyl fragment was drawn and optimised at the HF 3-21G level. Two of these fragments were constructed and placed one on top of the other facing apart in a rough chair conformation.
A Gaussian calculation was set up to to compute the transition state optimisation and frequency. The job ran well and the output file showed a single negative frequency at -818cm<sup>−1</sup> which corresponded to the expected cope rearrangement as can be seen below:

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 27;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>JWCHAIR_TS_1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

======Frozen Coordinate Method======

The alternative method for finding the transition state structure is to freeze the reaction coordinate except for the bond being broken and formed. The rest of the molecule is optimised to a minimum and then the bonds are optimised for the transition state.
This method has the advantage that the more complicated transition state calculation is limited to the bonds being broken and formed, so it can be a time saving technique.

The resulting transition state came out with an almost identical transition state structure as can be seen,

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>ChairTSpartd.mol</uploadedFileContents>
</jmolApplet></jmol>

The bond length of the bond forming/breaking was 2.02076A as opposed to 2.02054A which is pretty much the same within the level of accuracy of the calculation and the geometry in terms of bond angles was virtually indistinguishable.
This proves the idea that certainly in terms of this simple reaction these two methods to calculate the transition state are equally accurate.

=====Boat C<sub>2v</sub> transition state =====

To find the transition state structure a different method was used, the QST2 method works by inputing the starting and final product geometries and the computer will interpolate between the two to find the transition state structure. As with the two previous methods the computation will fail if you dont provide structures close to the optimum one. When the anti2 structure geometry was used the calculation was unsuccessful.
Using a more gauche starting structure successfully gave the following boat transition structure, which was confirmed with a vibration calculation which gave a negative frequency corresponding to the cope rearrangement.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>300</size>
<script>zoom 100;frame 37;vectors 2;vectors scale 2.0;color vectors red; vibration 4;
</script><uploadedFileContents>BOATGOODQST2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

=====Connecting the transition state geometry to the starting product geometry=====

From looking at the transition state it is difficult to tell what the geometry of the reactant and product is. However using the Intrinsic Reaction Coordinate method allows us to follow the potential energy surface to the local minima and hence the optimised geometry. The calculation from the chair transition state was given 50 steps but only 24 steps were used as can be seen in the following plot:
[[Image:JWChairIRC.jpg|none|300px| ]]

The geometry however still wasn't at a fully minimal geometry yet so the final product was further optimised using a regular optimisation calculation.

[[Image:IRCmin.jpg|thumb|200px| ]]

The result of this calculation was to give a structure with the same symmetry and energy as the Gauche2 structure. As seen here:

====Activation Energies====

The activation energy is the difference in the energy between the starting product and the transition state. However the level basis set used so far isn't very accurate for the energies, so the structures were first optimised to the higher level basis set B3LYP 6-31G(d).

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>CHAIR_TS_OPT631-3.mol</uploadedFileContents>
</jmolApplet></jmol>

This didn't change the geometries visibly as can be seen, but gave significantly lower energies. The energies obviously depend on the temperature. The difference in the Sum of electronic and thermal energies was to calculate the activation energy at room temperature and the Sum of electronic and zero-point energies was used to for the reaction at 0°K. To compare the activation energies with those found in the literature the energies were converted into Kcal/mol.

e.g for the chair transition state:

'''At Room Temperature:'''
-234.409009 - (-234.461856) = 0.052847
x 627.509
=33.16kcal/mol

'''At 0°K:'''
-234.414930 - (-234.469212) = 0.054282
x 627.509
=34.06kcal/mol

These results make sense as one would expect more energy to be required to overcome the activation barrier at a lower temperature.

The last value is very close to the literature value of 33.5 ± 0.5kcal/mol at 0°K (presumably from extrapolation as the reaction obviously can't be done at 0°K ) implying that the computational model is fairly accurate and presumably at a higher basis set it would be even more so.

Although for the boat structure the activation energy was a bit further off (41.96 kcal/mol vs 44.7 ± 2.0 kcal/mol) experimentally at 0°K.

These results imply that the cope reaction will kinetically go via the chair structure.

===Diels Alder===

In this part of the lab the same calculations as used for the cope rearrangement were used to find the transition state for a diels alder reaction, initially the most simple diels-alder reaction was computed and then a more complicated reaction with maleic anhydride was calculated and the calculation was used to explain the stereospecific nature of the reaction.

====Cis Butadiene and Ethene====

Initially the starting proeducts were drawn on gaussview and optimised
The cis butadiene starting product was constructed and the HOMO and LUMO orbitals visualised.
[[Image:CisbutadieneLUMO.jpg|thumb|200px|Cis butadiene LUMO]][[Image:CisbutadieneHOMO.jpg|thumb|200px|Cis butadiene HOMO]]]

The LUMO was found to be symmetric and the HOMO antisymmetric with respect to the plane of the molecule.