ChemWiki - User contributions [en]

Rep:Mod3ejc107

2010-03-26T14:50:01Z

Ejc107: /* The Cope Rearrangement */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the possible transition states located on the potential energy surface in the cope rearrangement:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on gradient anaylsis of steps taken along the reaction potential energy curve.

At a transition state a maximum in the potential energy surface will be observed and as of such a first derivative = 0. The second derivative is also important and will give a negative value. This is reflected in the vibrational frequencies and therefore a negative vibration.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant 1,5-hexadiene can be considered to be in a gauche or antiperplaner arrangement based on rotation around the central C-C bond.

Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method, so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 orginally calculated is the lowest in energy and the most stable, this is most likely due to steric interactions.

d-e)

The anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained aond point grup of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy was reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and gives values that are realistically comparable to one's experimentally obtained.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearrangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution at 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as they had been optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat structure and suggests the optimisation had correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932 || -231.46670 || -231.46134 || 0.07284 || 0.07123 || 45.71 || 44.69
|-
| Boat || -231.60280 || -231.45093 || -231.44530 || 0.08866 || 0.08727 || 55.61 || 54.76
|-
| Anti 2 || -231.69254 || -231.53954 || -231.53257
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698 || -234.41493 || -234.40901 || 0.04988 || 0.05283 || 31.30 || 33.15
|-
| Boat || -234.54309 || -234.40234 || -234.39601 || 0.06684 || 0.06583 || 41.94 || 41.31
|-
| Anti 2 || -234.61172 || -234.46918 || -234.46184
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisons were made with anti 2 however gauche 2, which the transition state resulted in or gauche 3, the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference's in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T14:46:43Z

Ejc107: /* Transition States */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative is also important and will give a negative value. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant 1,5-hexadiene can be considered to be in a gauche or antiperplaner arrangement based on rotation around the central C-C bond.

Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method, so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 orginally calculated is the lowest in energy and the most stable, this is most likely due to steric interactions.

d-e)

The anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained aond point grup of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy was reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and gives values that are realistically comparable to one's experimentally obtained.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearrangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution at 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as they had been optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat structure and suggests the optimisation had correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932 || -231.46670 || -231.46134 || 0.07284 || 0.07123 || 45.71 || 44.69
|-
| Boat || -231.60280 || -231.45093 || -231.44530 || 0.08866 || 0.08727 || 55.61 || 54.76
|-
| Anti 2 || -231.69254 || -231.53954 || -231.53257
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698 || -234.41493 || -234.40901 || 0.04988 || 0.05283 || 31.30 || 33.15
|-
| Boat || -234.54309 || -234.40234 || -234.39601 || 0.06684 || 0.06583 || 41.94 || 41.31
|-
| Anti 2 || -234.61172 || -234.46918 || -234.46184
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisons were made with anti 2 however gauche 2, which the transition state resulted in or gauche 3, the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference's in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T14:32:59Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative is also important and will give a negative value. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant 1,5-hexadiene can be considered to be in a gauche or antiperplaner arrangement based on rotation around the central C-C bond.

Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method, so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 orginally calculated is the lowest in energy and the most stable, this is most likely due to steric interactions.

d-e)

The anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained aond point grup of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy was reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and gives values that are realistically comparable to one's experimentally obtained.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearrangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932 || -231.46670 || -231.46134 || 0.07284 || 0.07123 || 45.71 || 44.69
|-
| Boat || -231.60280 || -231.45093 || -231.44530 || 0.08866 || 0.08727 || 55.61 || 54.76
|-
| Anti 2 || -231.69254 || -231.53954 || -231.53257
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698 || -234.41493 || -234.40901 || 0.04988 || 0.05283 || 31.30 || 33.15
|-
| Boat || -234.54309 || -234.40234 || -234.39601 || 0.06684 || 0.06583 || 41.94 || 41.31
|-
| Anti 2 || -234.61172 || -234.46918 || -234.46184
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisons were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T14:31:22Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative is also important and will give a negative value. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant 1,5-hexadiene can be considered to be in a gauche or antiperplaner arrangement based on rotation around the central C-C bond.

Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method, so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 orginally calculated is the lowest in energy and the most stable, this is most likely due to steric interactions.

d-e)

The anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained aond point grup of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy was reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and gives values that are realistically comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearrangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932 || -231.46670 || -231.46134 || 0.07284 || 0.07123 || 45.71 || 44.69
|-
| Boat || -231.60280 || -231.45093 || -231.44530 || 0.08866 || 0.08727 || 55.61 || 54.76
|-
| Anti 2 || -231.69254 || -231.53954 || -231.53257
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698 || -234.41493 || -234.40901 || 0.04988 || 0.05283 || 31.30 || 33.15
|-
| Boat || -234.54309 || -234.40234 || -234.39601 || 0.06684 || 0.06583 || 41.94 || 41.31
|-
| Anti 2 || -234.61172 || -234.46918 || -234.46184
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisons were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T14:23:19Z

Ejc107: /* The Cope Rearrangement */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative is also important and will give a negative value. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable, this is most likely due to steric interactions.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realistically comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearrangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932 || -231.46670 || -231.46134 || 0.07284 || 0.07123 || 45.71 || 44.69
|-
| Boat || -231.60280 || -231.45093 || -231.44530 || 0.08866 || 0.08727 || 55.61 || 54.76
|-
| Anti 2 || -231.69254 || -231.53954 || -231.53257
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698 || -234.41493 || -234.40901 || 0.04988 || 0.05283 || 31.30 || 33.15
|-
| Boat || -234.54309 || -234.40234 || -234.39601 || 0.06684 || 0.06583 || 41.94 || 41.31
|-
| Anti 2 || -234.61172 || -234.46918 || -234.46184
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisons were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T14:19:11Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable, this is most likely due to steric interactions.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realistically comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearrangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932 || -231.46670 || -231.46134 || 0.07284 || 0.07123 || 45.71 || 44.69
|-
| Boat || -231.60280 || -231.45093 || -231.44530 || 0.08866 || 0.08727 || 55.61 || 54.76
|-
| Anti 2 || -231.69254 || -231.53954 || -231.53257
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698 || -234.41493 || -234.40901 || 0.04988 || 0.05283 || 31.30 || 33.15
|-
| Boat || -234.54309 || -234.40234 || -234.39601 || 0.06684 || 0.06583 || 41.94 || 41.31
|-
| Anti 2 || -234.61172 || -234.46918 || -234.46184
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisons were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T14:18:35Z

Ejc107: /* Transition States */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable, this is most likely due to steric interactions.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realistically comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearrangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932 || -231.46670 || -231.46134 || 0.07284 || 0.07123 || 45.71 || 44.69
|-
| Boat || -231.60280 || -231.45093 || -231.44530 || 0.08866 || 0.08727 || 55.61 || 54.76
|-
| Anti 2 || -231.69254 || -231.53954 || -231.53257
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698 || -234.41493 || -234.40901 || 0.04988 || 0.05283 || 31.30 || 33.15
|-
| Boat || -234.54309 || -234.40234 || -234.39601 || 0.06684 || 0.06583 || 41.94 || 41.31
|-
| Anti 2 || -234.61172 || -234.46918 || -234.46184
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisions were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T14:17:51Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable, this is most likely due to steric interactions.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realistically comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932 || -231.46670 || -231.46134 || 0.07284 || 0.07123 || 45.71 || 44.69
|-
| Boat || -231.60280 || -231.45093 || -231.44530 || 0.08866 || 0.08727 || 55.61 || 54.76
|-
| Anti 2 || -231.69254 || -231.53954 || -231.53257
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698 || -234.41493 || -234.40901 || 0.04988 || 0.05283 || 31.30 || 33.15
|-
| Boat || -234.54309 || -234.40234 || -234.39601 || 0.06684 || 0.06583 || 41.94 || 41.31
|-
| Anti 2 || -234.61172 || -234.46918 || -234.46184
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisions were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T14:10:01Z

Ejc107: /* Transition States */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable, this is most likly due to steric interactions.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932 || -231.46670 || -231.46134 || 0.07284 || 0.07123 || 45.71 || 44.69
|-
| Boat || -231.60280 || -231.45093 || -231.44530 || 0.08866 || 0.08727 || 55.61 || 54.76
|-
| Anti 2 || -231.69254 || -231.53954 || -231.53257
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698 || -234.41493 || -234.40901 || 0.04988 || 0.05283 || 31.30 || 33.15
|-
| Boat || -234.54309 || -234.40234 || -234.39601 || 0.06684 || 0.06583 || 41.94 || 41.31
|-
| Anti 2 || -234.61172 || -234.46918 || -234.46184
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisions were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T14:06:30Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable, this is most likly due to steric interactions.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.46918 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.46184 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisions were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T13:54:39Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable, this is most likly due to steric interactions.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.469182 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.461842 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisions were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T13:51:05Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.469182 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.461842 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

It is clear that the chair transition state is lower in activation energy and therefore expected to be the dominant process. The comparisions were made with anti 2 however gauche 2 which the transition state resulted in or gauche 3 the lowest energy conformer might have been more appropriate

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:53:03Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.469182 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K as -234.461842 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:52:34Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.469182 Hartrees, -147131.52 kcal/mol and a thermal correction for 298.15K to -234.461842 Hartress, 147126.92 kcal/mol

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:50:25Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.469182 Hartrees, and a thermal correction for 298.15K to -234.461842 Hartress,

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:49:35Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234.469182 and a thermal correction for 298.15K to -234

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:48:58Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

This gives an energy at 0K of -234 and a thermal correction for 298.15K to -234

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:46:53Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both a conformation that the minima has been obtained (see earlier) and give values that are realisticly comparable to one's experimentally obtained results.

The frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:44:54Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step was then to try various gauche conformations and see the optimised energies

The result of this is that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:43:58Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

1 Hartree = 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:42:48Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. Soc. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:39:52Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies.
There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

It is important to note is that while direct comparison between two absolute energy values from two different basis sets is nonsense, energy difference's such as activation energies are allowed to be compared.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:37:40Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || [http://hdl.handle.net/10042/to-4802 DOI:10042/to-4802]
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:36:29Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| [http://hdl.handle.net/10042/to-4800 DOI:10042/to-4800] || cell
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:34:07Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairts631mol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>
|| <jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boatts631mol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

|-
| cell || cell
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:32:38Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

{| class="wikitable" border="1"
|+ 6-31g(d) Geometries
! Chair !! Boat
|-
| [[Image:ejc107chairts631.jpg|300px|Chair TS]] || [[Image:ejc107boatts631.jpg|300px|Boat TS]]
|-
| cell || cell
|-
| cell || cell
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

File:Ejc107boatts631mol.mol

2010-03-26T12:30:38Z

Ejc107:

File:Ejc107chairts631mol.mol

2010-03-26T12:30:25Z

Ejc107:

File:Ejc107boatts631.jpg

2010-03-26T12:30:13Z

Ejc107:

File:Ejc107chairts631.jpg

2010-03-26T12:30:01Z

Ejc107:

Rep:Mod3ejc107

2010-03-26T12:24:48Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier.

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised.

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d):

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:24:07Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactant used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set after the calculated transition states were reoptimised. The results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The Transition States for the 6-31g(d) are shown below:

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:21:05Z

Ejc107: /* Intrinsic Reaction Coordinate */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4799 DOI:10042/to-4799]

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:19:42Z

Ejc107: /* Intrinsic Reaction Coordinate */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:19:27Z

Ejc107: /* Intrinsic Reaction Coordinate */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>
[http://hdl.handle.net/10042/to-4798 DOI:10042/to-4798]

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:15:06Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>[http://pubs.acs.org/doi/pdf/10.1021/ja00101a078] O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:13:04Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>http://pubs.acs.org/doi/pdf/10.1021/ja00101a078 O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

==References==

<references/>

Rep:Mod3ejc107

2010-03-26T12:12:32Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment<ref name=copeexp>http://pubs.acs.org/doi/pdf/10.1021/ja00101a078 O. Wiest, K. A. Black, K. N. Houk, J. Am. Chem. SOC. 1994,116, 10336-10337</ref>
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T19:09:50Z

Ejc107: /* Activation energies */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energies defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T19:09:35Z

Ejc107: /* Intrinsic Reaction Coordinate */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likly to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energiess defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T19:09:15Z

Ejc107: /* Boat Tranistion State */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Transition State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Gaussian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geometries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likley to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energiess defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T19:08:23Z

Ejc107: /* Chair Transition State */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearrangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Tranistion State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Guassian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geomoetries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likley to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energiess defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T19:07:49Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energies

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Tranistion State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Guassian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geomoetries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likley to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energiess defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T19:06:19Z

Ejc107: /* The Cope Rearrangement */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearrangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first derivative = 0. The second derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energys

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Tranistion State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Guassian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geomoetries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likley to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energiess defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T19:04:24Z

Ejc107: /* Transition States */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first dervitive = 0. The secound derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energys

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Tranistion State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Guassian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geomoetries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likley to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 conformer resulting from the transition state. The conformer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energies====

Activation energiess defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accurately reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summarised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geometries from the 6-31g(d) optimisation are very similar however there are significant difference in the energies. Important to note is that while direct comparison between two absolute values from different basis sets is nonsense, energy difference such as activation energies can.

There is far closer correlation to the literature sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T19:02:13Z

Ejc107: /* Transition States */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first dervitive = 0. The secound derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energys

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangement is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The transition states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an initial calculation of a force constant matrix (Hessian) that is updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorporate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The transition state is highly similar to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearangement

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The second method involves fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant coordinate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtained with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the initial guess is quite close.

====Boat Tranistion State====

The boat transition state was calculated using the QST2 method, which is based on providing the reactant and product geometries and allowing Guassian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This job failed to converge on the desired transition state, so clearly the reactant and product molecules were not close enough to the transitions state for Gaussian to recognise the reaction procedure.

The reactant and product geomoetries were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the conformer the transition state will result in, however this can be calculated using the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calculated only once.

This resulted in a structure that hadn't properly converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was achieved by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more reliable. Giving the calculation more points is also likley to be less helpful as the calculation stopped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 confromer resulting from the transition state. The confromer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energys====

Activation energys defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accuratly reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summerised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geomoetries from the 6-31g(d) optimisation are very similer however there are significant difference in the energies. Important to note is that while direct comparision between two absolute values from different basis sets is nonsense, energy difference such as activation energys can.

There is far closer correlation to the litriture sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T18:53:51Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first dervitive = 0. The secound derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transition state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and gauche structures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using Gaussian resulted in the following structure:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be identified as Anti-1 from the lab appendix

b)

The next step was to optimise a gauche structure using the same basis set and method so that relative energies can be directly comparable.

The initial gauche conformer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This correlates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimisations the gauche conformation seems to be favoured slightly.

The next step then is to try various gauche conformations and see the optimised energys

The result of this that gauche 3 is the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was re-optimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energies as you should not directly compare energies from different basis sets.

The point group like before is reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimentally obtained results.

The Frequency calculation was carried out on the 6-31g(d) optimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant stretches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Stretches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relevant thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangment is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The Transtion states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an intial calculation of a force constant matrix (Hessian) thats updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorperate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The tranisition state is highly similer to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearangment

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The secound method invovles fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant corridnate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtianed with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the intial guess is quite close.

====Boat Tranistion State====

The boat transistion state was calculated using the QST2 method, which is based on providing the reactant and product geometrys and allowing guassian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This jobfailed to converge on the desired transition state, so clearly the reactant and prouct molcules were not close enough to the transitions state for Guassian to reconise the reaction procedure.

The reactant and product geomoetrys were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the confromer the transition state will result in, however this can be calculated using the the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calcuated only once.

This resulted in a structure that hadn't propally converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was acheived by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more relible. Giving the calulation more points is also likley to be less helpful as the calculation stoped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 confromer resulting from the transition state. The confromer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energys====

Activation energys defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accuratly reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summerised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geomoetries from the 6-31g(d) optimisation are very similer however there are significant difference in the energies. Important to note is that while direct comparision between two absolute values from different basis sets is nonsense, energy difference such as activation energys can.

There is far closer correlation to the litriture sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T18:46:42Z

Ejc107: /* The Cope Rearrangment */

==Module 3==

===The Cope Rearrangement===

The purpose of this module is the characterisation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearangement as well as the preferred reaction mechanism:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schrodinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient achieved.

At a transition state a maximum to the potential energy surface will be obtained and as of such a first dervitive = 0. The secound derivative also important will give a negative. This is reflected in the vibrational frequencies and therefore a negative vibration is expected.

The optimisation of reactants is to a minima on the potential energy surface, with all positive vibrational frequencies.

===Reactant Optimisation===

The first step in the location of the transistion state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and guache stuctures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using gaussian resulted in the folowing stucture:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be indentified as Anti-1 from the lab appendix

b)

The next step was to optimise a guache structure using the same basis set and method so that relitive energys can be directly comparable.

The intial gauche confromer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This corralates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimistations the guache confromation seems to be favoured slightly.

The next step then is to try varous gauche confromations and see the optimised energys

This results in gauche 3 being the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was reoptimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energys as you should not directly compare energys from different basis sets.

The point group like befores reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimantally obtained results.

The Frequency calcuation was carried out on the 6-31g(d) opptimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant streches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Streches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relavent thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangment is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The Transtion states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an intial calculation of a force constant matrix (Hessian) thats updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorperate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The tranisition state is highly similer to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearangment

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The secound method invovles fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant corridnate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtianed with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the intial guess is quite close.

====Boat Tranistion State====

The boat transistion state was calculated using the QST2 method, which is based on providing the reactant and product geometrys and allowing guassian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This jobfailed to converge on the desired transition state, so clearly the reactant and prouct molcules were not close enough to the transitions state for Guassian to reconise the reaction procedure.

The reactant and product geomoetrys were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the confromer the transition state will result in, however this can be calculated using the the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calcuated only once.

This resulted in a structure that hadn't propally converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was acheived by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more relible. Giving the calulation more points is also likley to be less helpful as the calculation stoped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 confromer resulting from the transition state. The confromer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energys====

Activation energys defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accuratly reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summerised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geomoetries from the 6-31g(d) optimisation are very similer however there are significant difference in the energies. Important to note is that while direct comparision between two absolute values from different basis sets is nonsense, energy difference such as activation energys can.

There is far closer correlation to the litriture sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T18:30:22Z

Ejc107: /* Reactant Optimisation */

==Module 3==

===The Cope Rearrangment===

The purpose of this module is the charactiszation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearangment as well as the prefered reaction mechanisum:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schroddinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient acheived.

At a transition state a maximiun to the potential energy surface will be obtained and as of such a first dervitive = 0. The Secound dervitive also important will give a negative. This is reflected in the vibrational frequencys and therefore a negative vibration is expected.

The optimisation of recatants is to a minima on the potential energy surface, with all positive vibrational frequencys.

===Reactant Optimisation===

The first step in the location of the transistion state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and guache stuctures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using gaussian resulted in the folowing stucture:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be indentified as Anti-1 from the lab appendix

b)

The next step was to optimise a guache structure using the same basis set and method so that relitive energys can be directly comparable.

The intial gauche confromer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This corralates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimistations the guache confromation seems to be favoured slightly.

The next step then is to try varous gauche confromations and see the optimised energys

This results in gauche 3 being the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was reoptimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
</jmolAppletButton>
</jmol>

The energy reported to be -234.61171040 Hartrees, -147220.96 kcal/mol however this is not directly comparable to previously quoted energys as you should not directly compare energys from different basis sets.

The point group like befores reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimantally obtained results.

The Frequency calcuation was carried out on the 6-31g(d) opptimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant streches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Streches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relavent thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangment is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The Transtion states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an intial calculation of a force constant matrix (Hessian) thats updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorperate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
</jmolAppletButton>
</jmol>

The tranisition state is highly similer to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearangment

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The secound method invovles fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant corridnate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairtsmodredmol.mol</uploadedFileContents>
<text>Chair TS 2nd Method Jmol</text>
</jmolAppletButton>
</jmol>

The same result as before was obtianed with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the intial guess is quite close.

====Boat Tranistion State====

The boat transistion state was calculated using the QST2 method, which is based on providing the reactant and product geometrys and allowing guassian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This jobfailed to converge on the desired transition state, so clearly the reactant and prouct molcules were not close enough to the transitions state for Guassian to reconise the reaction procedure.

The reactant and product geomoetrys were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
</jmolAppletButton>
</jmol>

This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the confromer the transition state will result in, however this can be calculated using the the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calcuated only once.

This resulted in a structure that hadn't propally converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
</jmolAppletButton>
</jmol>

The convergence was acheived by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more relible. Giving the calulation more points is also likley to be less helpful as the calculation stoped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 confromer resulting from the transition state. The confromer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107chairisc46mol.mol</uploadedFileContents>
<text>IRC - Gauche 2Jmol</text>
</jmolAppletButton>
</jmol>

[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energys====

Activation energys defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accuratly reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summerised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geomoetries from the 6-31g(d) optimisation are very similer however there are significant difference in the energies. Important to note is that while direct comparision between two absolute values from different basis sets is nonsense, energy difference such as activation energys can.

There is far closer correlation to the litriture sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.

Rep:Mod3ejc107

2010-03-25T18:26:40Z

Ejc107: /* Activation energys */

==Module 3==

===The Cope Rearrangment===

The purpose of this module is the charactiszation of the transition states located on the potential energy surface in the reaction coordinate of the cope rearangment as well as the prefered reaction mechanisum:

[[Image:ejc107cope.JPG|Cope Rearangment image]]

The calculations will involve MO methods and numerical solutions to the schroddinger as opposed to molecular mechanics methods which do not allow for the breaking and formation of bonds.

The calculations are based on the potential energy curves followed as the reaction steps progress and the gradient acheived.

At a transition state a maximiun to the potential energy surface will be obtained and as of such a first dervitive = 0. The Secound dervitive also important will give a negative. This is reflected in the vibrational frequencys and therefore a negative vibration is expected.

The optimisation of recatants is to a minima on the potential energy surface, with all positive vibrational frequencys.

===Reactant Optimisation===

The first step in the location of the transistion state is the calculation of the reactant geometry.

The reactant of the being 1,5-hexadiene and can be considered to be in a gauche or antiperplaner based on rotation around the central C-C bond. Rotations around the other C-C bonds leads to differing anti and guache stuctures:

[[Image:ejc107antigauche.JPG|1,5-hexadiene arrangments]]

a)

The first guess at a reactant was to try an antiperplaner structure and optimise it using a very simple Hartree-Fock method and the simple 3-21g(d) basis set.

Optimisation using gaussian resulted in the folowing stucture:

[[Image:ejc107anti1.jpg|300px|Anti 1]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>ejc107anti1mol.mol</uploadedFileContents>
<text>Anti 1 Conformer Jmol</text>
</jmolAppletButton>
</jmol>

The Energy recorded was = -231.69260235 Hartrees which can be converted to -145389.19kcal/mol

As one Hartree is 627.509kcal/mol

The point group was noted as C2 and can be indentified as Anti-1 from the lab appendix

b)

The next step was to optimise a guache structure using the same basis set and method so that relitive energys can be directly comparable.

The intial gauche confromer formed is shown below:

[[Image:ejc107gauche3.jpg|300px|Gauche 3]]

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<uploadedFileContents>ejc107gauche3mol.mol</uploadedFileContents>
<text>Gauche 3 Conformer Jmol</text>
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</jmol>

The energy obtained from this calculation was: -231.69266122 Hartrees

This corralates to an energy of -145389.23kcal/mol which can be seen to be of lower energy than the optimised anti conformer.

The point group was noted C1 and the conformation confirmed as Gauche 3 from the lab appendix

c)

From the above optimistations the guache confromation seems to be favoured slightly.

The next step then is to try varous gauche confromations and see the optimised energys

This results in gauche 3 being the lowest in energy and the most stable.

d-e)

The Anti 2 structure was optimised by the Hartree-Fock method with the 3-21g basis set

This resulted in:

[[Image:ejc107anti2.jpg|300px|Anti 2]]

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<uploadedFileContents>ejc107anti2mol.mol</uploadedFileContents>
<text>Anti 2 Conformer Jmol</text>
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An energy of -231.69253529 Hartrees / -145389.15kcal/mol was obtained and point group of Ci

f)

The anti 2 structure was reoptimised with a higher level basis set (6-31g(d)) to obtain a more accurate reactant geometry shown below:

[[Image:ejc107anti2631.jpg|300px|Anti 2 - 6-31g(d)]]

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<uploadedFileContents>ejc107anti2631mol.mol</uploadedFileContents>
<text>Anti 2 Conformer - 6-31g(d) Jmol</text>
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The energy reported to be -234.61171040 Hartrees however this is not directly comparable to previously quoted energys as you should not directly compare energys from different basis sets.

The point group like befores reported as Ci however the major difference in the structures is the angle of the central carbons, 112.67o compared to 111.35o see below:

[[Image:ejc107anti2angle.JPG|Angle Differences]]

g)

The final step in the optimisation of the reactants is a frequency calculation, which allows both conformation the minima has been obtained (see earlier) and give values that are realistic comparable to experimantally obtained results.

The Frequency calcuation was carried out on the 6-31g(d) opptimised structure using the same basis set.

The job return all positive and real vibrations, selected relevant streches are shown below along with an IR spectrum:

{| class="wikitable" border="1"
|+ Relevant Streches
! Wavenumber !! Infrared !! Vibration Image
|-
| 940.41 || 55.31 || [[Image:ejc107anti2s94041.JPG|200px|Stretch1]]
|-
| 3031.61 || 53.60 || [[Image:ejc107anti2s303161.JPG|200px|Stretch3]]
|-
| 3137.15 || 56.07 || [[Image:ejc107anti2s313715.JPG|200px|Stretch3]]
|-
| 3233.93 || 45.49 || [[Image:ejc107anti2s323393.JPG|200px|Stretch4]]
|}

IR Spectrum

[[Image:ejc107anti2IR.JPG|IR Spectrum]]

The output file from the vibrations listed the relavent thermochemical information shown below:

[[Image:ejc107anti2sumsfile.JPG|Log File Output]]

===Transition States===

The Cope rearangment is generally considered to go either by a chair or boat transition state:

[[Image:ejc107chairboat.JPG|Chair And Boat TS Image]]

The Transtion states for both the chair and boat can be considered to be constructed from 2 C3H5 allyl fragments

====Chair Transition State====

The chair transition state was modelled using two different methods but both centred around a predicted transition state from the combination of the two allyl fragments:

[[Image:ejc107chairtsguess.jpg|300px|Constructed TS
]]

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<uploadedFileContents>ejc107chairtsguessmol.mol</uploadedFileContents>
<text>Chair TS Jmol</text>
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Note: The distance between the fragments was estimated at 2.2A

The first method for optimisation of the chair transition state involves an intial calculation of a force constant matrix (Hessian) thats updated during the optimisation.

Hartree-Fock method with a 3-21g basis set was used for an optimisation and frequency calculation to a ts(berny). The force constants were set to only be calculated once rather than in every step and the calculation was set to incorperate the possibility of more than one imaginary frequency.

The resultant structure is shown below:

[[Image:ejc107chairts.jpg|300px|Chair TS
]]

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<text>Chair TS Jmol</text>
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The tranisition state is highly similer to the predicted transition state however the distance between the two allyl fragments has been reduced to 2.02A

The frequency showed one imaginary solution as 818cm-1, which can be seen to be relate to the bond forming in the cope rearangment

[[Image:ejc107chairtscope.JPG|Cope Frequency]]

The secound method invovles fixing the reaction coordinate for the important bond forming places and optimising the rest of the structure. The reaction coordinate then can be optimised to a transition state with less hessian calculations and potentially time saving.

The restriction was made so that the two allyl fragments were 2.2A apart using the redundant corridnate editor. The optimisation to a minimum and then to a ts(berny) used a Hartree-Fock method with 3-21g basis set.

The results are shown below:

[[Image:ejc107chairtsmodred.jpg|300px|Chair ts]]

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<text>Chair TS 2nd Method Jmol</text>
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The same result as before was obtianed with a inter-allyl distance of 2.02A. This is expected as both methods are optimising to the same transition state and the intial guess is quite close.

====Boat Tranistion State====

The boat transistion state was calculated using the QST2 method, which is based on providing the reactant and product geometrys and allowing guassian to go back and forth to indentify the transition state.

The reactants and products selected were based on the anti 2 structure. The first trial was to use them just as optimised.

This jobfailed to converge on the desired transition state, so clearly the reactant and prouct molcules were not close enough to the transitions state for Guassian to reconise the reaction procedure.

The reactant and product geomoetrys were then therefore improved to closer match the transition structure by modifying the dihedral from 180oto 0o and and central carbon angles from 111o to 100o:

[[Image:ejc107boattsrp.JPG|600px|Reactant and Products for Boat TS]]

This QST2 calculation gave the following transition state:

[[Image:ejc107boatts.JPG|300px|Boat TS
]]

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<uploadedFileContents>ejc107boattsmol.mol</uploadedFileContents>
<text>Boat TS Jmol</text>
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This seems to represent the boat transition state and suggests the optimisations has correctly converged

====Intrinsic Reaction Coordinate====

From the transition structures alone it is hard to determine the confromer the transition state will result in, however this can be calculated using the the intrinsic reaction coordinate method.

The method takes a set number (50 was chosen) of steps down the steepest potential energy gradient. The force constants were chosen to be calcuated only once.

This resulted in a structure that hadn't propally converged:

[[Image:ejc107chiarirc.jpg|300px|Chair ISC
]]

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<uploadedFileContents>ejc107chairiscmol.mol</uploadedFileContents>
<text>Initial Chair IRC Jmol</text>
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The convergence was acheived by recalculating the IRC with force constants at every point. This is more computationally heavy than optimising the currently obtained structure to a minimum however considered more relible. Giving the calulation more points is also likley to be less helpful as the calculation stoped after 27 steps anyway.

The IRC involved 47 steps and the revealed the gauche 2 confromer resulting from the transition state. The confromer is best seen in the penultimate step.

[[Image:ejc107chairirc462.jpg|300px|Chair ISC gauche 2
]]

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<text>IRC - Gauche 2Jmol</text>
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[[Image:ejc107chairircgraph.JPG|Chair ISC graph's
]]

The point group of the IRC product is noted as C2

====Activation energys====

Activation energys defined as the distance between the reactants and the transition state can be calculated for the 3-21G basis set. The reactants used is the anti 2 conformer recorded earlier. Results shown below:

{| class="wikitable" border="1"
|+ 3-21g Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -231.61932244 || -231.466700 || -231.461341 || 0.072841 || 0.071225 || 45.71 || 44.69
|-
| Boat || -231.60280247 || -231.450927 || -231.445297 || 0.0886614 || 0.087269 || 55.61 || 54.76
|-
| Anti 2 || -231.6925353 || -231.539541 || -231.532566
|}

This however could be more accuratly reported using the 6-31g(d) higher level basis set and results are shown below:

{| class="wikitable" border="1"
|+ 6-31g(d) Energies
! Structure !! Electronic Energy !! Sum of electronic and zero-point energies (a.u.) (0K) !! Sum of electronic and thermal energies (a.u.) (298.15K) !! Activation Energy (a.u.) 0K !! Activation Energy (a.u.) 298.15K !! Activation Energy (kcal/mol) 0K !! Activation Energy (kcal/mo) 298.15K
|-
| Chair || -234.55698303 || -234.414930 || -234.409009 || 0.049882 || 0.052833 || 31.30 || 33.15
|-
| Boat || -234.54309307 || -234.402342 || -234.396008 || 0.06684 || 0.065834 || 41.94 || 41.31
|-
| Anti 2 || -234.61172096 || -234.469182 || -234.461842
|}

The activation energies at 0K compared to experiment can be summerised as below:

{| class="wikitable" border="1"
|+ Summary 0K
! TS !! Activation 3-21g (kcal/mol) !! Activation 6-31g(d) (kcal/mol)!! Experiment
|-
| Chair || 45.71 || 31.30 || 33.5 ± 0.5
|-
| Boat || 55.61 || 41.94 || 44.7 ± 2.0
|}

The geomoetries from the 6-31g(d) optimisation are very similer however there are significant difference in the energies. Important to note is that while direct comparision between two absolute values from different basis sets is nonsense, energy difference such as activation energys can.

There is far closer correlation to the litriture sources in the 6-31g(d), this is due to the higher accuracy of both the B3LYP method and the higher 6-31g(d) basis set.