ChemWiki - User contributions [en]

Rep:Mod:jem3i

2010-12-17T14:17:40Z

Jem08: /* Cope Rearrangement */

==Jenifer Mizen: Transition States and Reactivity (Module 3)==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated here.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
.[[Image:lennardjones.jpg|right|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:

<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form
The lowest energy conformation (D) was then optimised and is shown below:

<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:-818imaginarychairtsberny.gif|widthpx|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===
[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: C-C bond forming distance: 2.20A, C-C bonds 1.40A, C-C-C angle: 122.4<sup>o</sup>.
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory. The main difference was the increased C-C bond forming length.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. The previous data found at the lower level of optimisation was: C-C bond forming distance 2.14A, C-C bond lengths 1.38A, C-C-C angle 121.6<sup>o</sup>. Again, the main difference was the increased C-C bond forming distance.

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol).

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

File:-818imaginarychairtsberny.gif

2010-12-16T18:13:07Z

Jem08:

Rep:Mod:jem3i

2010-12-16T18:12:45Z

Jem08: /* Chair */

==Jenifer Mizen: Transition States and Reactivity (Module 3)==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated here.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:-818imaginarychairtsberny.gif|widthpx|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===
[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: C-C bond forming distance: 2.20A, C-C bonds 1.40A, C-C-C angle: 122.4<sup>o</sup>.
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory. The main difference was the increased C-C bond forming length.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. The previous data found at the lower level of optimisation was: C-C bond forming distance 2.14A, C-C bond lengths 1.38A, C-C-C angle 121.6<sup>o</sup>. Again, the main difference was the increased C-C bond forming distance.

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol).

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

File:-818imaginarychairtsberny.jpg

2010-12-16T18:11:50Z

Jem08:

Rep:Mod:jem3i

2010-12-16T16:15:24Z

Jem08: /* Cope Rearrangement */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChairMovie.gif|widthpx|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===
[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: C-C bond forming distance: 2.20A, C-C bonds 1.40A, C-C-C angle: 122.4<sup>o</sup>.
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory. The main difference was the increased C-C bond forming length.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. The previous data found at the lower level of optimisation was: C-C bond forming distance 2.14A, C-C bond lengths 1.38A, C-C-C angle 121.6<sup>o</sup>. Again, the main difference was the increased C-C bond forming distance.

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol).

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

Rep:Mod:jemwiki

2010-12-16T15:16:09Z

Jem08: New page: ==The Diels Alder Cycloaddtion== Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=buta...

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|100px|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|100px|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was asymmetrical with respect to the reflection plane of the reaction the mole, and the LUMO was symmetric.

[[Image:cis_butadieneHOMOa.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMOa.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds, then TS(Berny)calculation was used.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1. Visualising this frequency suggested that both bonds formed at the same time. The lowest positive frequency was 165cm<sup>-1</sup>. This would have suggested asynchronous bond formation.

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 29.3
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The dihedral angle was the main difference in geometry.
The Mos were also visualised using the more accurate basis set, however there were no significant changes. The imaginary frequency did however change to 311cm<sup>-1</sup>, and the lowest positive frequency to 116cm<sup>-1</sup>. The imaginary frequency appear the same, but the positive one was less conclusively asynchronous at the higher level.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

The thermochemistry data did change considerably:
Zero-point correction= 0.141771 (Hartree/Particle)
Thermal correction to Energy= 0.147361
Thermal correction to Enthalpy= 0.148305
Thermal correction to Gibbs Free Energy= 0.112772
Sum of electronic and zero-point Energies= -234.369822
Sum of electronic and thermal Energies= -234.364233
Sum of electronic and thermal Enthalpies= -234.363289
Sum of electronic and thermal Free Energies= -234.398822

The HOMO of ethene is symmetric with respect to the reflection plane, whereas its LUMO is antisymmetric. A reaction is allowed if a HOMO-LUMO interaction between the reactants is possible. Since a + a --> a, s + s --> and s + a --> a, the product must be antisymmetric with respect to the reflection plane.
This can be seen in the TS:
[[Image:antisymhomo.jpg|centre|thumb|200px|]]
This is confirmed by looking at the MOs of the cis1,3-butadiene. The LUMO reacts with the HOMO orbital of the ethene to give the TS. The HOMO/LUMO interaction and the fact that there is good orbital overlap means that the reaction is allowed.

==Cyclohexa-1,3-diene and Maleic Anhydride==
==Exo TS==
The exo TS was optimised and thermochemistry data found:
Zero-point correction= 0.195859 (Hartree/Particle)
Thermal correction to Energy= 0.204620
Thermal correction to Enthalpy= 0.205564
Thermal correction to Gibbs Free Energy= 0.161353
Sum of electronic and zero-point Energies= -605.383190
Sum of electronic and thermal Energies= -605.374429
Sum of electronic and thermal Enthalpies= -605.373485
Sum of electronic and thermal Free Energies= -605.417696

[[Image:exosummary.jpg|centre|thumb|200px|optimisation summary]][[Image:exoenergygradient.jpg|centre|thumb|200px|optimisation energy gradient]]

[[Image:exoTS.jpg|centre|thumb|200px|TS]]
[[Image:exoa.gif|centre|thumb|200px|Imaginary vibration at -110cm<sup>-1</sup>.]]

Bond lengths were investigated, and will be compared with the endo TS (see later).

The TS HOMO was found:
[[Image:exohomo.jpg|centre|thumb|200px|HOMO]]

....................Bond forming lengths 1.69A, 1.54A. The HOMO is therefore not totally symmetrical and doesn’t have a perfect C2 axis or sigma v plane. C-C distances in maleic anhydride part: (C1-2 and C3-4)1.51 and 1.52
C13-14: 1.49
C14-15: 1.32
C15-10: 1.53
C10-11: 1.69
C11-12: 1.55
C12-13: 1.54

(CO)-O-(CO): 112.7o......................... 63.2
==Endo TS==
A QST3 calculation was done on the following input at the HF/3-21g level: [[Image:endoinput.jpg|centre|thumb|200px|endo input]]
[[Image:endoHFsummary.jpg|centre|thumb|200px|output summary]]
One negative vibration was found at -644cm-1. This showed concerted bond formation.[[Image:endo.gif|centre|thumb|200px|endo input]]
The lowest positive frequency 65cm-1 consisted of the cyclohexene ring rotating in its plane: [[Image:endoHFpositivefrequency.jpg|centre|thumb|200px|endo 1st positive frequency]]

HOMO:
LUMO of maleic anhydride overlaps with HOMO of double bonds in cyclohexadiene to make the bonds that are forming:
[[Image:endoHFHOMO.jpg|centre|thumb|200px|HOMO]]
There was symmetry down the axis which cuts the middle oxygen – but with reserve phase either side. This time, there was a little more electron density on the oxygens of malaic anhydride compared to in the exo TS.
LUMO:
[[Image:endoHFLUMO.jpg|centre|thumb|200px|LUMO]]

In the LUMO, the phase was reversed for the cyclohexadiene, so that it no longer interacts with the orbitals of the malaic anhydride double bond, and nodes were formed at the four participating carbons and in the middle of the forming bond.
==DFT calculations==
The transition states were re-optimised using the DFT method.
Exo: -612.68339676
Zero-point correction= 0.181256 (Hartree/Particle)
Thermal correction to Energy= 0.191609
Thermal correction to Enthalpy= 0.192554
Thermal correction to Gibbs Free Energy= 0.145069
Sum of electronic and zero-point Energies= -612.502141
Sum of electronic and thermal Energies= -612.491787
Sum of electronic and thermal Enthalpies= -612.490843
Sum of electronic and thermal Free Energies= -612.538327

Endo:
Zero-point correction= 0.181253 (Hartree/Particle)
Thermal correction to Energy= 0.191607
Thermal correction to Enthalpy= 0.192551
Thermal correction to Gibbs Free Energy= 0.145069
Sum of electronic and zero-point Energies= -612.502143
Sum of electronic and thermal Energies= -612.491790
Sum of electronic and thermal Enthalpies= -612.490846
Sum of electronic and thermal Free Energies= -612.538328

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope=”col” | C-C bond forming length
! scope="col" | 1-2
! scope="col" | 3-4
! scope="col" | 13-14
! scope="col" | 14-15
! scope="col" | 15-10
! scope="col" | 10-11
! scope="col" | 11-12
! scope="col" | 12-13
|-
! scope="row" | exo HF/3-21g
|
| 1.51
| 1.52
| 1.49
| 1.32
| 1.53
| 1.69
| 1.55
| 1.54
|-
! scope="row" | endo HF/3-21g
|
| 1.48
| 1.48
| 1.37
| 1.40
| 1.37
| 1.52
| 1.56
| 1.52
|-
! scope=”row”| endo 3BLYP/6-21g(d)
| 2.27
| 1.48
| 1.39
| 1.49
| 1.39
| 1.52
| 1.56
|1.56
| 1.52
|}

In the HF/3-21G calculations, for the exo configuration, the through space angle between (CO) – O-(CO) and the opposite –CH2-CH2- was 63.2o. For the endo, the same angle, but for the opposite –CH=CH- was -54.4o.
The angles after the 3BYLP/6-21g(d) changed to and 54.8o respectively.
The Mos changed to the following:
[[Image:endoHOMOdft.jpg|centre|thumb|200px|HOMO]] [[Image:endoLUMOdft.jpg|centre|thumb|200px|LUMO]]

[[Image:endoTScontributingMOs.jpg|centre|thumb|200px|Possible allowed ways of constructing the endo TS]]

compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo and secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.

Rep:Mod:jem3i

2010-12-16T12:39:27Z

Jem08: /* Chair */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChairMovie.gif|widthpx|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===
[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: C-C bond forming distance: 2.20A, C-C bonds 1.40A, C-C-C angle: 122.4<sup>o</sup>.
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory. The main difference was the increased C-C bond forming length.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. The previous data found at the lower level of optimisation was: C-C bond forming distance 2.14A, C-C bond lengths 1.38A, C-C-C angle 121.6<sup>o</sup>. Again, the main difference was the increased C-C bond forming distance.

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol).

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

Rep:Mod:jem3i

2010-12-16T12:37:53Z

Jem08: /* Chair */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChairMovie.gif|200px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===
[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: C-C bond forming distance: 2.20A, C-C bonds 1.40A, C-C-C angle: 122.4<sup>o</sup>.
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory. The main difference was the increased C-C bond forming length.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. The previous data found at the lower level of optimisation was: C-C bond forming distance 2.14A, C-C bond lengths 1.38A, C-C-C angle 121.6<sup>o</sup>. Again, the main difference was the increased C-C bond forming distance.

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol).

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

Rep:Mod:jem3i

2010-12-16T12:37:20Z

Jem08:

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|150px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===
[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: C-C bond forming distance: 2.20A, C-C bonds 1.40A, C-C-C angle: 122.4<sup>o</sup>.
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory. The main difference was the increased C-C bond forming length.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. The previous data found at the lower level of optimisation was: C-C bond forming distance 2.14A, C-C bond lengths 1.38A, C-C-C angle 121.6<sup>o</sup>. Again, the main difference was the increased C-C bond forming distance.

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol).

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

Rep:Mod:jem3i

2010-12-16T12:12:45Z

Jem08: /* Activation energies for the reaction via both boat and chair TS */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===
[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. The previous data found at the lower level of optimisation was: C-C bond forming distance 2.14A, C-Cbond lengths

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol).

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

Rep:Mod:jem3i

2010-12-16T11:59:42Z

Jem08: /* Activation energies for the reaction via both boat and chair TS */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===
[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. The previous data found at the lower level of optimisation was: C-C bond forming distance 2.14A, C-Cbond lengths

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

Rep:Mod:jem3i

2010-12-16T11:41:39Z

Jem08: /* Boat */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===
[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

Rep:Mod:jem3i

2010-12-16T11:40:29Z

Jem08: /* Boat */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.
[[Image:TSBoatQST3.jpg|left|thumb|widthpx|TS found by QST3]]
The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

File:TSBoatQST3.jpg

2010-12-16T11:39:18Z

Jem08:

File:TSBoatQST3a.mol

2010-12-16T11:38:38Z

Jem08:

Rep:Mod:jem3i

2010-12-16T11:34:36Z

Jem08: /* Boat */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the configurations shown.[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the structure shown.
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

<jmol><jmolApplet><title>lQST3 TS optimisation</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatQST3.mol</uploadedFileContents> </jmolApplet></jmol>

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

Rep:Mod:jem3i

2010-12-16T11:33:20Z

Jem08: /* Boat */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. Initially the QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. In this case, the exact geometries of the structures inputted were not quite as important as for QST2. This gave the TS structure shown, and C2v symmetry.

<jmol><jmolApplet><title>lQST3 TS optimisation</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatQST3.mol</uploadedFileContents> </jmolApplet></jmol>

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together, and it resembles the TS the closest.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

Rep:Mod:jem3i

2010-12-16T11:22:22Z

Jem08: /* Chair */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration and the TS are shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line was shown between the carbons, instead of one double and one single bond. This did not appear using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising.
This time, the distance between the terminal carbons of each fragment was set to 2.2A. The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

Rep:Mod:jem3i

2010-12-16T11:17:01Z

Jem08: /* Cope Rearrangement */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|left|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

File:Anti2IR.jpg

2010-12-16T11:16:10Z

Jem08:

Rep:Mod:jem3i

2010-12-16T11:10:13Z

Jem08:

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
The transition structure of the Cope rearragement was investigated.
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar (a.p.p.) relationship between the four middle carbon atoms was optimised using HF/3-21G (a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>However the optimised energy was found -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction was responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation (D) was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the more accurate B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. This meant that additional thermochemistry data could be found, as well as the IR frequencies. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.
[[Image:anti2IR.jpg|left|thumb|100px|Anit2 IR spectrum]]

Thermochemistry data:
Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

Rep:Mod:jem3i

2010-12-16T10:46:33Z

Jem08: /* Boat */

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==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:qst2boatinput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

File:Qst2boatinput.jpg

2010-12-16T10:44:37Z

Jem08:

File:Thermochemistry data at different temperatures.jpg

2010-12-15T17:46:27Z

Jem08:

Rep:Mod:jem3i

2010-12-15T17:42:15Z

Jem08:

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==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

Activation energies(kcal/mol):

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | low level method, 0K
! scope="col" | low level method, 298.15K
! scope="col" | high level method, 0K
! scope="col" | high level method, 298.15K
|-
! scope="row" | chair
| 45.71
| 44.69
| 33.82
| 33.76
|-
! scope="row" | boat
| 55.60
| 54.76
| 73.95
| 73.29
|-
|}

Experimental values at 0K were 33.5 +- 0.5 for the chair and 44.7+-2.0 for the boat.
The values found for the boat at the higher level of optimisation were very different, suggesting that this calculation may not have worked. However for the chair, the higher level shows the value the same as the experimental one for the higher level of calculation (whereas it is incorrect at the lower level). The activation energy for the boat was higher than that for the chair, however the calculated activation energies were very different to the experimental ones.

It was also possible to investigate the thermochemistry data at different temperatures using the FreqChk utility in Gaussian3. The corrections at 500K are shown as an example:
[[Image:thermochemistry_data_at_different_temperatures.jpg|left|thumb|widthpx|thermochemistry data at different temperatures]]

ATTACH APPENDICES.

Rep:Mod:jem3ii

2010-12-15T16:16:15Z

Jem08:

Rep:Mod:jem3i

2010-12-15T15:58:28Z

Jem08:

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<comment>/* The Diels Alder Cycloaddtion */</comment>
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<text xml:space="preserve">
==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

Rep:Mod:jem3ii

2010-12-15T15:58:14Z

Rep:Mod:jem3i

2010-12-15T15:57:33Z

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<page>
<title>Mod:jem3</title>
<id>34543</id>
−
<revision>
<id>134999</id>
<timestamp>2010-12-15T11:20:35Z</timestamp>
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<contributor>
<username>Jem08</username>
<id>343</id>
</contributor>
<comment>/* The Diels Alder Cycloaddtion */</comment>
−
<text xml:space="preserve">
==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|100px|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|100px|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was asymmetrical with respect to the reflection plane of the reaction the mole, and the LUMO was symmetric.

[[Image:cis_butadieneHOMOa.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMOa.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds, then TS(Berny)calculation was used.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1. Visualising this frequency suggested that both bonds formed at the same time. The lowest positive frequency was 165cm<sup>-1</sup>. This would have suggested asynchronous bond formation.

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 29.3
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The dihedral angle was the main difference in geometry.
The Mos were also visualised using the more accurate basis set, however there were no significant changes. The imaginary frequency did however change to 311cm<sup>-1</sup>, and the lowest positive frequency to 116cm<sup>-1</sup>. The imaginary frequency appear the same, but the positive one was less conclusively asynchronous at the higher level.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

The thermochemistry data did change considerably:
Zero-point correction= 0.141771 (Hartree/Particle)
Thermal correction to Energy= 0.147361
Thermal correction to Enthalpy= 0.148305
Thermal correction to Gibbs Free Energy= 0.112772
Sum of electronic and zero-point Energies= -234.369822
Sum of electronic and thermal Energies= -234.364233
Sum of electronic and thermal Enthalpies= -234.363289
Sum of electronic and thermal Free Energies= -234.398822

The HOMO of ethene is symmetric with respect to the reflection plane, whereas its LUMO is antisymmetric. A reaction is allowed if a HOMO-LUMO interaction between the reactants is possible. Since a + a --> a, s + s --> and s + a --> a, the product must be antisymmetric with respect to the reflection plane.
This can be seen in the TS:
[[Image:antisymhomo.jpg|centre|thumb|200px|]]
This is confirmed by looking at the MOs of the cis1,3-butadiene. The HOMO reacts with the pi antibonding orbital of the ethene to give the TS. The HOMO/LUMO interaction and the fact that there is good orbital overlap means that the reaction is allowed.
</text>
</revision>
</page>
</mediawiki>

Rep:Mod:jem3

2010-12-15T12:11:39Z

Jem08: /* Exo TS */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|100px|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|100px|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was asymmetrical with respect to the reflection plane of the reaction the mole, and the LUMO was symmetric.

[[Image:cis_butadieneHOMOa.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMOa.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds, then TS(Berny)calculation was used.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1. Visualising this frequency suggested that both bonds formed at the same time. The lowest positive frequency was 165cm<sup>-1</sup>. This would have suggested asynchronous bond formation.

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 29.3
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The dihedral angle was the main difference in geometry.
The Mos were also visualised using the more accurate basis set, however there were no significant changes. The imaginary frequency did however change to 311cm<sup>-1</sup>, and the lowest positive frequency to 116cm<sup>-1</sup>. The imaginary frequency appear the same, but the positive one was less conclusively asynchronous at the higher level.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

The thermochemistry data did change considerably:
Zero-point correction= 0.141771 (Hartree/Particle)
Thermal correction to Energy= 0.147361
Thermal correction to Enthalpy= 0.148305
Thermal correction to Gibbs Free Energy= 0.112772
Sum of electronic and zero-point Energies= -234.369822
Sum of electronic and thermal Energies= -234.364233
Sum of electronic and thermal Enthalpies= -234.363289
Sum of electronic and thermal Free Energies= -234.398822

The HOMO of ethene is symmetric with respect to the reflection plane, whereas its LUMO is antisymmetric. A reaction is allowed if a HOMO-LUMO interaction between the reactants is possible. Since a + a --> a, s + s --> and s + a --> a, the product must be antisymmetric with respect to the reflection plane.
This can be seen in the TS:
[[Image:antisymhomo.jpg|centre|thumb|200px|]]
This is confirmed by looking at the MOs of the butadiene. The HOMO reacts with the pi antibonding orbital of the ethene to give the TS. The HOMO/LUMO interaction and the fact that there is good orbital overlap means that the reaction is allowed.

==Cyclohexa-1,3-diene and maleic anhydride==

Next, the reaction of cyclohex-1,3-diene with maleic anhydride was investigated. The endo and exo TS structures were optimised and geometries and energies compared.

Firstly, the cyclohexadiene was optimised at HF/3-21g level and was seen to converge.[[Image:cyclohexadieneopt1summary.jpg|centre|thumb|200px|Cyclohexadiene HF/3-21g optimisation summary]]
[[Image:cyclohexadieneopt1energygradient.jpg|centre|thumb|200px|Cyclohexadiene HF/3-21g optimisation energy gradient]]. Next, this was reoptimised at B3LYP?6-31G(d) and convergence checked as before. The same was done for maleic anhydride.

Once the two reactants were optimised satisfactorily, the endo and exo products were optimised.
A QST3 calculation could then be set up, with the optimised reactants in one pane, the product in the next, and a guessed structure for the TS in the last pane. Data from a previous computational experiment REFERENCE HERE was used to guess suitable bond forming lengths for the TS, and the atoms were re-numbered appropriately.

J.I. Garcia, J.A. Mayoral, and Luis Salvatella, "An Ab Initio Study on the Conformational and Endo/Exo Preference of Acrylate in Diels-Alder Reactions", Tetrahedron, 53, 6057 (1997).

==Exo TS==
The exo TS was optimised and thermochemistry data found:
Zero-point correction= 0.195859 (Hartree/Particle)
Thermal correction to Energy= 0.204620
Thermal correction to Enthalpy= 0.205564
Thermal correction to Gibbs Free Energy= 0.161353
Sum of electronic and zero-point Energies= -605.383190
Sum of electronic and thermal Energies= -605.374429
Sum of electronic and thermal Enthalpies= -605.373485
Sum of electronic and thermal Free Energies= -605.417696

[[Image:exosummary.jpg|centre|thumb|200px|optimisation summary]][[Image:exoenergygradient.jpg|centre|thumb|200px|optimisation energy gradient]]

[[Image:exoTS.jpg|centre|thumb|200px|TS]]
[[Image:exoa.gif|centre|thumb|200px|Imaginary vibration at -110cm<sup>-1</sup>.]]

Bond lengths were investigated, and will be compared with the endo TS (see later).

The TS HOMO was found:
[[Image:exohomo.jpg|centre|thumb|200px|HOMO]]

....................Bond forming lengths 1.69A, 1.54A. The HOMO is therefore not totally symmetrical and doesn’t have a perfect C2 axis or sigma v plane. C-C distances in maleic anhydride part: (C1-2 and C3-4)1.51 and 1.52
C13-14: 1.49
C14-15: 1.32
C15-10: 1.53
C10-11: 1.69
C11-12: 1.55
C12-13: 1.54

(CO)-O-(CO): 112.7o.........................

==Endo TS==

File:Exoa.gif

2010-12-15T12:10:49Z

Jem08:

File:ExoHOMO.jpg

2010-12-15T12:10:05Z

Jem08:

File:ExoTS.jpg

2010-12-15T12:08:17Z

Jem08:

File:Exoenergygradient.jpg

2010-12-15T12:07:41Z

Jem08:

File:Exosummary.jpg

2010-12-15T12:07:13Z

Jem08:

Rep:Mod:jem3

2010-12-15T11:59:38Z

Jem08: /* Cyclohexa-1,3-diene and maleic anhydride */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|100px|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|100px|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was asymmetrical with respect to the reflection plane of the reaction the mole, and the LUMO was symmetric.

[[Image:cis_butadieneHOMOa.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMOa.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds, then TS(Berny)calculation was used.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1. Visualising this frequency suggested that both bonds formed at the same time. The lowest positive frequency was 165cm<sup>-1</sup>. This would have suggested asynchronous bond formation.

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 29.3
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The dihedral angle was the main difference in geometry.
The Mos were also visualised using the more accurate basis set, however there were no significant changes. The imaginary frequency did however change to 311cm<sup>-1</sup>, and the lowest positive frequency to 116cm<sup>-1</sup>. The imaginary frequency appear the same, but the positive one was less conclusively asynchronous at the higher level.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

The thermochemistry data did change considerably:
Zero-point correction= 0.141771 (Hartree/Particle)
Thermal correction to Energy= 0.147361
Thermal correction to Enthalpy= 0.148305
Thermal correction to Gibbs Free Energy= 0.112772
Sum of electronic and zero-point Energies= -234.369822
Sum of electronic and thermal Energies= -234.364233
Sum of electronic and thermal Enthalpies= -234.363289
Sum of electronic and thermal Free Energies= -234.398822

The HOMO of ethene is symmetric with respect to the reflection plane, whereas its LUMO is antisymmetric. A reaction is allowed if a HOMO-LUMO interaction between the reactants is possible. Since a + a --> a, s + s --> and s + a --> a, the product must be antisymmetric with respect to the reflection plane.
This can be seen in the TS:
[[Image:antisymhomo.jpg|centre|thumb|200px|]]
This is confirmed by looking at the MOs of the butadiene. The HOMO reacts with the pi antibonding orbital of the ethene to give the TS. The HOMO/LUMO interaction and the fact that there is good orbital overlap means that the reaction is allowed.

==Cyclohexa-1,3-diene and maleic anhydride==

Next, the reaction of cyclohex-1,3-diene with maleic anhydride was investigated. The endo and exo TS structures were optimised and geometries and energies compared.

Firstly, the cyclohexadiene was optimised at HF/3-21g level and was seen to converge.[[Image:cyclohexadieneopt1summary.jpg|centre|thumb|200px|Cyclohexadiene HF/3-21g optimisation summary]]
[[Image:cyclohexadieneopt1energygradient.jpg|centre|thumb|200px|Cyclohexadiene HF/3-21g optimisation energy gradient]]. Next, this was reoptimised at B3LYP?6-31G(d) and convergence checked as before. The same was done for maleic anhydride.

Once the two reactants were optimised satisfactorily, the endo and exo products were optimised.
A QST3 calculation could then be set up, with the optimised reactants in one pane, the product in the next, and a guessed structure for the TS in the last pane. Data from a previous computational experiment REFERENCE HERE was used to guess suitable bond forming lengths for the TS, and the atoms were re-numbered appropriately.

J.I. Garcia, J.A. Mayoral, and Luis Salvatella, "An Ab Initio Study on the Conformational and Endo/Exo Preference of Acrylate in Diels-Alder Reactions", Tetrahedron, 53, 6057 (1997).

==Exo TS==
The exo TS was optimised and thermochemistry data found:
Zero-point correction= 0.195859 (Hartree/Particle)
Thermal correction to Energy= 0.204620
Thermal correction to Enthalpy= 0.205564
Thermal correction to Gibbs Free Energy= 0.161353
Sum of electronic and zero-point Energies= -605.383190
Sum of electronic and thermal Energies= -605.374429
Sum of electronic and thermal Enthalpies= -605.373485
Sum of electronic and thermal Free Energies= -605.417696

[[Image:exosummary.jpg|centre|thumb|200px|optimisation summary]][[Image:exoenergygradient.jpg|centre|thumb|200px|optimisation energy gradient]]

[[Image:exoTS.jpg|centre|thumb|200px|TS]]
[[Image:exo.gif|centre|thumb|200px|Imaginary vibration at -110cm<sup>-1</sup>.]]

Bond lengths were investigated, and will be compared with the endo TS (see later).

The TS HOMO was found:
[[Image:exohomo.jpg|centre|thumb|200px|HOMO]]

....................Bond forming lengths 1.69A, 1.54A. The HOMO is therefore not totally symmetrical and doesn’t have a perfect C2 axis or sigma v plane. C-C distances in maleic anhydride part: (C1-2 and C3-4)1.51 and 1.52
C13-14: 1.49
C14-15: 1.32
C15-10: 1.53
C10-11: 1.69
C11-12: 1.55
C12-13: 1.54

(CO)-O-(CO): 112.7o.........................

==Endo TS==

Rep:Mod:jem3

2010-12-15T11:58:18Z

Jem08: /* The Diels Alder Cycloaddtion */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|100px|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|100px|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was asymmetrical with respect to the reflection plane of the reaction the mole, and the LUMO was symmetric.

[[Image:cis_butadieneHOMOa.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMOa.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds, then TS(Berny)calculation was used.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1. Visualising this frequency suggested that both bonds formed at the same time. The lowest positive frequency was 165cm<sup>-1</sup>. This would have suggested asynchronous bond formation.

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 29.3
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The dihedral angle was the main difference in geometry.
The Mos were also visualised using the more accurate basis set, however there were no significant changes. The imaginary frequency did however change to 311cm<sup>-1</sup>, and the lowest positive frequency to 116cm<sup>-1</sup>. The imaginary frequency appear the same, but the positive one was less conclusively asynchronous at the higher level.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

The thermochemistry data did change considerably:
Zero-point correction= 0.141771 (Hartree/Particle)
Thermal correction to Energy= 0.147361
Thermal correction to Enthalpy= 0.148305
Thermal correction to Gibbs Free Energy= 0.112772
Sum of electronic and zero-point Energies= -234.369822
Sum of electronic and thermal Energies= -234.364233
Sum of electronic and thermal Enthalpies= -234.363289
Sum of electronic and thermal Free Energies= -234.398822

The HOMO of ethene is symmetric with respect to the reflection plane, whereas its LUMO is antisymmetric. A reaction is allowed if a HOMO-LUMO interaction between the reactants is possible. Since a + a --> a, s + s --> and s + a --> a, the product must be antisymmetric with respect to the reflection plane.
This can be seen in the TS:
[[Image:antisymhomo.jpg|centre|thumb|200px|]]
This is confirmed by looking at the MOs of the butadiene. The HOMO reacts with the pi antibonding orbital of the ethene to give the TS. The HOMO/LUMO interaction and the fact that there is good orbital overlap means that the reaction is allowed.

==Cyclohexa-1,3-diene and maleic anhydride==

Next, the reaction of cyclohex-1,3-diene with maleic anhydride was investigated. The endo and exo TS structures were optimised and geometries and energies compared.

Firstly, the cyclohexadiene was optimised at HF/3-21g level and was seen to converge.[[Image:cyclohexadieneopt1summary.jpg|centre|thumb|200px|Cyclohexadiene HF/3-21g optimisation summary]]
[[Image:cyclohexadieneopt1energygradient.jpg|centre|thumb|200px|Cyclohexadiene HF/3-21g optimisation energy gradient]]. Next, this was reoptimised at B3LYP?6-31G(d) and convergence checked as before. The same was done for maleic anhydride.

Once the two reactants were optimised satisfactorily, the endo and exo products were optimised.
A QST3 calculation could then be set up, with the optimised reactants in one pane, the product in the next, and a guessed structure for the TS in the last pane. Data from a previous computational experiment REFERENCE HERE was used to guess suitable bond forming lengths for the TS, and the atoms were re-numbered appropriately.

==Exo TS==
The exo TS was optimised and thermochemistry data found:
Zero-point correction= 0.195859 (Hartree/Particle)
Thermal correction to Energy= 0.204620
Thermal correction to Enthalpy= 0.205564
Thermal correction to Gibbs Free Energy= 0.161353
Sum of electronic and zero-point Energies= -605.383190
Sum of electronic and thermal Energies= -605.374429
Sum of electronic and thermal Enthalpies= -605.373485
Sum of electronic and thermal Free Energies= -605.417696

[[Image:exosummary.jpg|centre|thumb|200px|optimisation summary]][[Image:exoenergygradient.jpg|centre|thumb|200px|optimisation energy gradient]]

[[Image:exoTS.jpg|centre|thumb|200px|TS]]
[[Image:exo.gif|centre|thumb|200px|Imaginary vibration at -110cm<sup>-1</sup>.]]

Bond lengths were investigated, and will be compared with the endo TS (see later).

The TS HOMO was found:
[[Image:exohomo.jpg|centre|thumb|200px|HOMO]]

....................Bond forming lengths 1.69A, 1.54A. The HOMO is therefore not totally symmetrical and doesn’t have a perfect C2 axis or sigma v plane. C-C distances in maleic anhydride part: (C1-2 and C3-4)1.51 and 1.52
C13-14: 1.49
C14-15: 1.32
C15-10: 1.53
C10-11: 1.69
C11-12: 1.55
C12-13: 1.54

(CO)-O-(CO): 112.7o.........................

==Endo TS==

File:Antisymhomo.jpg

2010-12-15T11:26:56Z

Jem08:

Rep:Mod:jem3

2010-12-15T11:20:35Z

Jem08: /* The Diels Alder Cycloaddtion */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|100px|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|100px|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was asymmetrical with respect to the reflection plane of the reaction the mole, and the LUMO was symmetric.

[[Image:cis_butadieneHOMOa.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMOa.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds, then TS(Berny)calculation was used.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1. Visualising this frequency suggested that both bonds formed at the same time. The lowest positive frequency was 165cm<sup>-1</sup>. This would have suggested asynchronous bond formation.

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 29.3
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The dihedral angle was the main difference in geometry.
The Mos were also visualised using the more accurate basis set, however there were no significant changes. The imaginary frequency did however change to 311cm<sup>-1</sup>, and the lowest positive frequency to 116cm<sup>-1</sup>. The imaginary frequency appear the same, but the positive one was less conclusively asynchronous at the higher level.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

The thermochemistry data did change considerably:
Zero-point correction= 0.141771 (Hartree/Particle)
Thermal correction to Energy= 0.147361
Thermal correction to Enthalpy= 0.148305
Thermal correction to Gibbs Free Energy= 0.112772
Sum of electronic and zero-point Energies= -234.369822
Sum of electronic and thermal Energies= -234.364233
Sum of electronic and thermal Enthalpies= -234.363289
Sum of electronic and thermal Free Energies= -234.398822

The HOMO of ethene is symmetric with respect to the reflection plane, whereas its LUMO is antisymmetric. A reaction is allowed if a HOMO-LUMO interaction between the reactants is possible. Since a + a --> a, s + s --> and s + a --> a, the product must be antisymmetric with respect to the reflection plane.
This can be seen in the TS:
[[Image:antisymhomo.jpg|centre|thumb|200px|]]
This is confirmed by looking at the MOs of the cis1,3-butadiene. The HOMO reacts with the pi antibonding orbital of the ethene to give the TS. The HOMO/LUMO interaction and the fact that there is good orbital overlap means that the reaction is allowed.

Rep:Mod:jem3

2010-12-15T10:56:59Z

Jem08: /* The Diels Alder Cycloaddtion */

File:Cis butadieneLUMOa.jpg

2010-12-15T10:21:04Z

Jem08:

File:Cis butadieneHOMOa.jpg

2010-12-15T10:20:44Z

Jem08:

Rep:Mod:jem3

2010-12-15T10:20:18Z

Jem08: /* The Diels Alder Cycloaddtion */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|100px|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|100px|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was approximately symmetrical with respect to the "plane", and the LUMO antisymmetric.

[[Image:cis_butadieneHOMOa.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMOa.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. These were lined up in 3 windows, but the QST methods were grayed out ...?? so TS(Berny) was used. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1.
[[Image:TS(Berny)vibration.jpg|left|thumb|widthpx|imaginary frequency]]

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 0.052
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The Mos were also visualised using the more accurate basis set, however there were no significant changes.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

blahblahblah

File:Cisbutadiene LUMOa.jpg

2010-12-15T10:19:44Z

Jem08:

File:Cisbutadiene HOMOa.jpg

2010-12-15T10:19:30Z

Jem08:

Rep:Mod:jem3

2010-12-15T10:18:16Z

Jem08: /* The Diels Alder Cycloaddtion */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|100px|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|100px|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was approximately symmetrical with respect to the "plane", and the LUMO antisymmetric.

[[Image:cis_butadieneHOMO.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMO.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. These were lined up in 3 windows, but the QST methods were grayed out ...?? so TS(Berny) was used. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1.
[[Image:TS(Berny)vibration.jpg|left|thumb|widthpx|imaginary frequency]]

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 0.052
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The Mos were also visualised using the more accurate basis set, however there were no significant changes.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

blahblahblah

Rep:Mod:jem3

2010-12-14T15:45:59Z

Jem08:

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|widthpx|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|widthpx|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was approximately symmetrical with respect to the "plane", and the LUMO antisymmetric.

[[Image:cis_butadieneHOMO.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMO.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. These were lined up in 3 windows, but the QST methods were grayed out ...?? so TS(Berny) was used. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1.
[[Image:TS(Berny)vibration.jpg|left|thumb|widthpx|imaginary frequency]]

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 0.052
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The Mos were also visualised using the more accurate basis set, however there were no significant changes.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

blahblahblah

Rep:Mod:jem3

2010-12-14T11:06:04Z

Jem08: /* Optimising the Chair and Boat Transition Structures */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|widthpx|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|widthpx|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was approximately symmetrical with respect to the "plane", and the LUMO antisymmetric.

[[Image:cis_butadieneHOMO.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMO.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. These were lined up in 3 windows, but the QST methods were grayed out ...?? so TS(Berny) was used. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1.
[[Image:TS(Berny)vibration.jpg|left|thumb|widthpx|imaginary frequency]]

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 0.052
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The Mos were also visualised using the more accurate basis set, however there were no significant changes.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

Rep:Mod:jem3

2010-12-14T11:05:08Z

Jem08: /* Optimising the Chair and Boat Transition Structures */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

3. The calculation was repeated and force constants were calculated at each step.
<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|widthpx|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|widthpx|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was approximately symmetrical with respect to the "plane", and the LUMO antisymmetric.

[[Image:cis_butadieneHOMO.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMO.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. These were lined up in 3 windows, but the QST methods were grayed out ...?? so TS(Berny) was used. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1.
[[Image:TS(Berny)vibration.jpg|left|thumb|widthpx|imaginary frequency]]

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 0.052
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The Mos were also visualised using the more accurate basis set, however there were no significant changes.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.

Rep:Mod:jem3

2010-12-14T11:03:39Z

Jem08: /* Optimising the Chair and Boat Transition Structures */

==Jenifer Mizen: Transition States and Reactivity==

==Cope Rearrangement==
[[Image:pic1.jpg|right|thumb|Cope rearrangement]]<ref name=coperearrangement>Chemistry wiki {{www.ch.ic.ac.uk/wiki}}</ref>
[[Image:appenergygradient.jpg|left|thumb|100px|A.p.p energy gradient]]

Firstly, 1,5-hexadiene with an approximately anitiperiplanar relationship between the four middle carbon atoms was optimised using HF/3-21G ( a Hartree-Fock method with the 3-21G basis set).
The energy found by the summary was -231.68540au and the molecule was found to have C2h symmetry. The energy gradient and output files were both checked to ensure that convergence had been achieved.

Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000697 0.001200 YES
Predicted change in Energy=-2.752863D-07
Optimization completed.
-- Stationary point found.

This was repeated for a molecule in which the central carbons were gauche to each other. The energy was expected to be higher, as the a.p.p. conformation is generally the lowest in energy due to favourable interaction between the C-C (or C-H)σ-orbital and the neighbouring C-C (or C-H) σ*-orbital. The orbital overlap is best for the a.p.p. conformation compared to e.g. gauche.<ref name=conformationalanalysis>R. Pitzer, W. Lipscomb, ''J. Chem. Phys.'', '''1963''', ''39'', 1995. {{DOI|10.1063/1.1734572}}</ref>The optimised energy was -231.69153 au and the symmetry was C2.
[[Image:app.jpg|left|thumb|widthpx|One sigma bonding orbital can interact with another sigma antibonding orbital (shown in blue) in the antiperiplanar conformation]]

The two conformations are shown below:

<jmol><jmolApplet><title>A.p.p</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>hexadiene.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>gauche‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche.mol</uploadedFileContents> </jmolApplet></jmol>

[[Image:AppSummary.jpg|left|thumb|100px|A.p.p summary]]
[[Image:GaucheSummary.jpg|left|thumb|100px|Gauche summary]]
The gauche structure corresponds to Gauche4 in Appendix 1. The initial antiperiplanar structure had the same symmetry as Anti3, but a different structure and slightly different energy. It was most similar to Anti1. A slightly different starting geometry was used and optimised to the anti1 conformation:
<jmol><jmolApplet><title>Antiperiplanar 1</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>Anti_1.mol</uploadedFileContents> </jmolApplet></jmol>
This then gave the same point group and energy as anti1.

The Gauche structure was lower in energy than the antiperiplanar. This can be rationalised by considering the pi orbital interacting with the vicinal proton. Newman projections make it easier to visualise this interaction. Here, "D" corresponds to the minimum energy conformation (i.e. gauche 3 in the appendix 1).
[[Image:newmanprojections.jpg|right|thumb|100px|Newman projections]].<ref name=newmanprojections>B. Gung, Z. Zhu, R. Fouch, ''J. am. Chem. Soc.'', '''1995''', ''117'', 1783-1788. {{DOI|10.1021/ja00111a016}}</ref>
In the gauche form it was found that the distance between the terminal hydrogen (on the double bond) and a hydrogen on the third carbon atom was 2.44A, which corresponds to a van der Waals attractive interaction, (an A<sup>1,3</sup> eclipsed conformation).
Overall, the σ-C-H/π*C=C interaction is responsible for the lower energy of the gauche form.[[Image:lennardjones.jpg|centre|thumb|widthpx|van der Waals interaction distances]]<ref name=rzepa>H. Rzepa,{{|http://vle.imperial.ac.uk/webct/cobaltMainFrame.dowebct}}</ref>
[[Image:Anti2OptSummary.jpg|left|thumb|100px|A.p.p 2 summary]]
[[Image:Anti2Opt2Summary.jpg|left|thumb|100px|A.p.p 2 second optimisation summary]]

The lowest energy conformation was then optimised and is shown below:
<jmol><jmolApplet><title>Gauche 3</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>gauche3.mol</uploadedFileContents> </jmolApplet></jmol>
This has the same energy and point group as gauche 3 in appendix 1.
[[Image:gauche3optsummary.jpg|left|thumb|100px|Gauche 3 optimisation summary]]

Next, the Ci anti2 conformation was optimised, and the symmetry checked to ensure it had stayed the same. The energy was found to be -231.69254au. This is the same as that given in the table.
The molecule was then re-optimised, this time using the B3LYP/6-31G* level. The energy became more negative at -234.55970au.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | 1234 dihedral angle /<sup>o</sup>
! scope="col" | 2345 dihedral angle /<sup>o</sup>
! scope="col" | 1-2 & 5-6 bond length /A
! scope="col" | 2-3 and 4-5 bond length /A
! scope="col" | 3-4 bond length/A
|-
! scope="row" | 1st optimisation
| 114.7
| 180.0
| 1.32
| 1.51
| 1.55
|-
! scope="row" | 2nd optimisation
| 118.7
| 180.0
| 1.34
| 1.51
| 1.56
|-
|}

<jmol><jmolApplet><title>1st optimisation</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><title>2nd optimisation‎</title><color>pink</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>HEXADIENEANTI2OPT2.mol</uploadedFileContents> </jmolApplet></jmol>

For both, the 1234 dihedral angle was the same magnitude, but a different sign to the 3456 dihedral angle. This angle increased somewhat on the second optimisation, but there were no other particularly significant changes to the geometry.

Next, a frequency analysis was done using the same B3LYP/6-31G* level. No negative frequencies were found, with the lowest being at 71.69cm<sup>-1</sup>.

Sum of electronic and zero-point energies (potential energy at 0K) = -234.416244 au.

Sum of electronic and thermal energies (energy at 298.15K and 1atm, with contributions from translational, vibrational and rotational energy modes) = -234.408953 au.

Sum of electronic and thermal enthalpies (with correction for RT, H=E+RT) = -234.408009au.

Sum of electronic and thermal Free Energies (including entropy G=H-TS) = -234.447852.

--------------------------------------------------------------------------------------

PUT IR HERE
RECALCULATE AT 0K IF TIME
WHY AREN'T MY ANTI2 RESULTS THE SAME AS IN THE TABLE?

==Optimising the Chair and Boat Transition Structures==

===Chair===

Firstly, the allyl fragment was optimised (HF/3-21G). Then two of the optimised fragments were put together to give the approximate structure of the transition state. This was then optimised using two different methods:

1. Computing the force constant matrix (or the Hessian). This works well if the guess of the TS is very similar to the true structure.

HF/3-21G was used as before, and an Opt+Freq calculation done , with optimisation set to TS(Berny). To ensure that it did not crash if more than one imaginary frequency were found, "Opt=NoEigen" was added in the additional keywords section.
An imaginary frequency was found at 818cm<sup>-1</sup>. The vibration is shown below:

[[Image:TSChariMovie.gif|left|thumb|25px|click for chair TS imaginary vibration]]

[[Image:TSChairMovie.gif|50px|centre]]

<jmol><jmolApplet><title>TSforChairOptforwiki.mol‎</title><color>black</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSforChair.mol</uploadedFileContents> </jmolApplet></jmol>
On Gaussview, a dotted line is shown between the carbons, instead of one double and one single bond. This has not appeared using the jmol view, however the "single" and "double" bonds shown are actually the same length.

2. Freezing the reaction coordinate (so the rest of the molecule can be optimised), then unfreezing and re-optimising. This time, the distance between the terminal carbons of each fragment was set to 2.2A.

The molecule was then re-optimised to give a result identical to when using the previous method.
The distance between the terminal allyl carbons i.e. where the new bond will form, was found to be 2.02A.

===Boat===

Next, the boat TS was optimised. The QST2 method was used. Two of the Ci anti2 molecules previously optimised were used and the atoms numbered so that the reactant and the product labelling matched. An Opt+Freq calculation was done, and the job failed, giving the following output:
<jmol><jmolApplet><title>Failed optimisation for boat TS.mol‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>TSBoatFailed.mol</uploadedFileContents> </jmolApplet></jmol>

QST2 did not take into account the possibility of rotation about the central bonds, so failed to find the TS structure. The input was therefore modified so that the reactant (left hand side) and product (right hand side) had the following configurations:[[Image:TSBoatInput.jpg|left|thumb|widthpx|New input configurations for finding boat TS]]
The QST2 job was re-run. This gave error number 2070, and, when the .chk file was opened, Gaussview stopped responding. When the .out file was opened, it gave a "Gaussian error detected line number 1314" message, and the following structure:
[[Image:QST22ndtry.jpg|left|thumb|widthpx|TS found by QST2]]

This has evidently not worked either. QST2 is very sensitive to how close the inputted structures are to the TS, so there may have been an error in the input file.

The calculation was redone using QST3, and providing a guess for the TS. This gave the TS structure shown, and C2v symmetry. The C-H interactions shown are unexpected, with lengths of 2.7 and 3.4A.
[[Image:TSBoatQST3results.jpg|left|thumb|widthpx|TS found by QST3]]

The Gauche1 conformation in Appendix 1 appears to be the most suitable for the Cope rearrangement, as the two terminal carbons are closest together. The Anti2 also looks suitable, especially for the chair TS, as only a simple rotation around the centre C-C bond is needed to bring it into a suitable geometry for the bond breaking and making of the rearrangement.

===IRC===

Next, the intrinsic reaction coordinate method (IRC) was used.

<jmol><jmolApplet><title>Chair TS initial IRC‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC.mol</uploadedFileContents> </jmolApplet></jmol>

The first time this was used, a minimum geometry was not reached and the calculation was redone using three different methods:

1. The final structure given after the initial IRC was run was optimised.

<jmol><jmolApplet><title>Method 1.‎</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(i).mol</uploadedFileContents> </jmolApplet></jmol>

2. The IRC calculation was repeated with 100 points (doubling the number compared to the initial calculation).

<jmol><jmolApplet><title>Method 2.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(ii).mol</uploadedFileContents> </jmolApplet></jmol>

3. The calculation was repeated and force constants were calculated at each step.

<jmol><jmolApplet><title>Method 3.</title><color>cyan</color> <size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script> <uploadedFileContents>ChairTS+IRC(iii).mol</uploadedFileContents> </jmolApplet></jmol>

Method 3. should be the most reliable, however it took the longest amount of time to run.

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C forming bond length/A
|-
! scope="row" | Initial IRC
| 1.57, 2.90
|-
! scope="row" | IRC method 1.
| 2.17, 4.39
|-
! scope="row" | IRC method 2.
| 1.56, 3.28
|-
! scope="row" | IRC method 3.
| 2.02, 2.02
|-
|}

The bond forming length found using method 3. is the same as when the TS was optimised previously. This, and the result from the QST3 method both suggest concerted reactions, whereas the other methods do not.

===Activation energies for the reaction via both boat and chair TS===

The TS structures were reoptimised using the B3LYP/6-31G(d) level, starting from the HF/3-21G Hessian method optimised structures already found.
Geometries:
Chair: COMP TO NEW TS
This compares to the 2.02A, 1.39A and 120.5<sup>o</sup> found at the lower level of theory.
Boat:
C-C bond forming distance 2.23A for both pairs of carbons. All other C-C bonds 1.38A. C-C-C bond angle 122.6<sup>o</sup>. COMP TO PREVIOUS TS

Chair:
Initial lower level optimisation:
Zero-point correction= 0.152623 (Hartree/Particle)
Thermal correction to Energy= 0.157983
Thermal correction to Enthalpy= 0.158927
Thermal correction to Gibbs Free Energy= 0.124771
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.494551

Higher level optimisation:
Total energy from summary file -234.55868305au
Zero-point correction= 0.143369 (Hartree/Particle)
Thermal correction to Energy= 0.150625
Thermal correction to Enthalpy= 0.151569
Thermal correction to Gibbs Free Energy= 0.111606
Sum of electronic and zero-point Energies= -234.415314
Sum of electronic and thermal Energies= -234.408058
Sum of electronic and thermal Enthalpies= -234.407114
Sum of electronic and thermal Free Energies= -234.447077

There were no imaginary vibrations in the IR.

Boat:
Lower level optimisation:
Zero-point correction= 0.151870 (Hartree/Particle)
Thermal correction to Energy= 0.157500
Thermal correction to Enthalpy= 0.158444
Thermal correction to Gibbs Free Energy= 0.123025
Sum of electronic and zero-point Energies= -231.450932
Sum of electronic and thermal Energies= -231.445303
Sum of electronic and thermal Enthalpies= -231.444359
Sum of electronic and thermal Free Energies= -231.479777

Higher level optimisation:
Total energy from summary file -232.79730444au
Zero-point correction= 0.141550 (Hartree/Particle)
Thermal correction to Energy= 0.147856
Thermal correction to Enthalpy= 0.148800
Thermal correction to Gibbs Free Energy= 0.112783
Sum of electronic and zero-point Energies= -234.351364
Sum of electronic and thermal Energies= -234.345059
Sum of electronic and thermal Enthalpies= -234.344114
Sum of electronic and thermal Free Energies= -234.380132

There was one imaginary vibration in the IR at -504.28cm<sup>-1</sup>.

These energies are significantly different to each other at the two different levels (1 Hartree = 627.509 kcal/mol). COMP TO APPENDIX 2

ACTIVATION ENERGIES ... AND AT HIGHER TEMPERATURES

ATTACH APPENDICES.

==The Diels Alder Cycloaddtion==

Firstly, cis butadiene was built in Gaussview and C-C bond lengths and angles were set using data from a previous molecular mechanics study.<ref name=butadienebondlengths>D. Guay,Dept of Chemistry, University of Maine, Orono, ME 04469{{|http://chemistry.umeche.maine.edu/Modeling/donmolmech.html }}</ref> This was "cleaned" then optimised to a minimum using HF/3-21G. The energy gradient and summary suggested that this had been successful. A frequency analysis was done using the same methods and no negative frequencies were found.
[[Image:cisbutadieneoptsummary.jpg|left|thumb|widthpx|cis butadiene optimisation summary]]
[[Image:cisbutadieneoptenergygradient.jpg|right|thumb|widthpx|cis butadiene optimisation energy gradient]]
[[Image:cisbutadienefreqsummary.jpg|left|thumb|widthpx|cis butadiene frequency summary]]
The thermochemistry data is shown below:
Zero-point correction= 0.118498 (Hartree/Particle)
Thermal correction to Energy= 0.122530
Thermal correction to Enthalpy= 0.123474
Thermal correction to Gibbs Free Energy= 0.092955
Sum of electronic and zero-point Energies= -155.112862
Sum of electronic and thermal Energies= -155.108830
Sum of electronic and thermal Enthalpies= -155.107886
Sum of electronic and thermal Free Energies= -155.138405

Next, the Mos were visualised. The HOMO was approximately symmetrical with respect to the "plane", and the LUMO antisymmetric.

[[Image:cis_butadieneHOMO.jpg|centre|thumb|widthpx|cis butadiene HOMO]][[Image:cis_butadieneLUMO.jpg|centre|thumb|widthpx|cis butadiene LUMO]]

Next, the optimised structure and ethene were drawn, and a TS guessed. These were lined up in 3 windows, but the QST methods were grayed out ...?? so TS(Berny) was used. The TS was guessed by modifying bicyclo[2,2,2]octane, deleting 2 carbons and changing or deleting other bonds.

TS(Berny) Optimisation:
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000421 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-5.010461D-09
Optimization completed.
-- Stationary point found.

The output gave 1 imaginary frequency at -554cm-1.
[[Image:TS(Berny)vibration.jpg|left|thumb|widthpx|imaginary frequency]]

[[Image:TS(Berny).gif|left|thumb|widthpx|imaginary frequency]]

The thermochemistry data is also shown below:
Zero-point correction= 0.152697 (Hartree/Particle)
Thermal correction to Energy= 0.157712
Thermal correction to Enthalpy= 0.158656
Thermal correction to Gibbs Free Energy= 0.124359
Sum of electronic and zero-point Energies= -231.388077
Sum of electronic and thermal Energies= -231.383062
Sum of electronic and thermal Enthalpies= -231.382118
Sum of electronic and thermal Free Energies= -231.416414

The Mos were then visualised. Both were found to have a sigma v plane of symmetry relative to the plane of the forming ring, and a C2 axis lying along this plane.
[[Image:TS(Berny)HOMO.jpg|centre|thumb|widthpx|TS HOMO]]
[[Image:TS(Berny)LUMO.jpg|centre|thumb|widthpx|TS LUMO]]

The above calculations were re-done using a higher level (B3LYP/6-31G(d) - outputs were checked as before)to give the following results:

{| border="1" style="margin-centre: 3em;"
|-
! scope="col" |
! scope="col" | C-C bond forming length/A
! scope="col" | C-C (from ethene) bond length/A
! scope="col" | C=C bond forming length/A
! scope="col" | C-C (from butadiene) lengths/A
! scope="col" | Butadiene dihedral angle/<sup>o</sup>
|-
! scope="row" | 1st optimisation
| 1.5
| 1.5
| 1.5
| 1.5
| 0.052
|-
! scope="row" | 2nd optimisation
| 1.5
| 1.6
| 1.6
| 1.5
| 22.2
|-
|}

The Mos were also visualised using the more accurate basis set, however there were no significant changes.

A normal C-C bond has length 1.54A, and C=C 1.36A. The van der Waals radius of carbon is 1.70A (Webelements). This means that the distance between the carbons about to form a new bond in the TS is less than that of the sum of the van der Waals radii.