ChemWiki - User contributions [en]

Rep:Mod:DAAO phys

2010-03-26T01:09:49Z

Da907: /* References */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="dft">Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI|10.1021/ja00101a078}}</ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

The output file provides details such as those shown below which will enable the activation energy of the Cope rearrangement to be calculated later in this report.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2 method. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å for both distances. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart as the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The IRC reaction coordinate vs RMS gradient is the very useful. It shows that the the gradient had not yet reached zero and so a minimum on the PES had not been found. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the same energy to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm or disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is said to be more reliable than Approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' conformer, this structure has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

Just we saw for Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the Cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of structures otptimised at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at a low level of theory followed by a higher level has been demonstrated throughout the report. It was seen that very slight changes in the geometry have markedly different energies. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 methods. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally, the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy at both 0 and 298.15K and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

[[User:Da907|Da907]] 01:09, 26 March 2010 (UTC)

Rep:Mod:DAAO phys

2010-03-26T01:09:17Z

Da907: /* The Cope Rearrangement Tutorial */

Rep:Mod:DAAO phys

2010-03-26T01:06:46Z

Da907: /* Conclusion */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

The output file provides details such as those shown below which will enable the activation energy of the Cope rearrangement to be calculated later in this report.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2 method. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å for both distances. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart as the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The IRC reaction coordinate vs RMS gradient is the very useful. It shows that the the gradient had not yet reached zero and so a minimum on the PES had not been found. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the same energy to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm or disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is said to be more reliable than Approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' conformer, this structure has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

Just we saw for Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the Cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of structures otptimised at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at a low level of theory followed by a higher level has been demonstrated throughout the report. It was seen that very slight changes in the geometry have markedly different energies. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 methods. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally, the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy at both 0 and 298.15K and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T01:01:41Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

The output file provides details such as those shown below which will enable the activation energy of the Cope rearrangement to be calculated later in this report.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2 method. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å for both distances. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart as the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The IRC reaction coordinate vs RMS gradient is the very useful. It shows that the the gradient had not yet reached zero and so a minimum on the PES had not been found. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the same energy to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm or disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is said to be more reliable than Approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' conformer, this structure has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

Just we saw for Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the Cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of structures otptimised at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:58:37Z

Da907: /* Approach 3: Redo IRC Computing Force Constants at Every Step */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

The output file provides details such as those shown below which will enable the activation energy of the Cope rearrangement to be calculated later in this report.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2 method. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å for both distances. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart as the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The IRC reaction coordinate vs RMS gradient is the very useful. It shows that the the gradient had not yet reached zero and so a minimum on the PES had not been found. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the same energy to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm or disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is said to be more reliable than Approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' conformer, this structure has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

Just we saw for Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:56:11Z

Da907: /* Approach 3: Redo IRC Computing Force Constants at Every Step */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

The output file provides details such as those shown below which will enable the activation energy of the Cope rearrangement to be calculated later in this report.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2 method. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å for both distances. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart as the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The IRC reaction coordinate vs RMS gradient is the very useful. It shows that the the gradient had not yet reached zero and so a minimum on the PES had not been found. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the same energy to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm or disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is said to be more reliable than Approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' conformer, this structure has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:55:04Z

Da907: /* Approach 2: Restart IRC & Increase Number of Iterations */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

The output file provides details such as those shown below which will enable the activation energy of the Cope rearrangement to be calculated later in this report.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2 method. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å for both distances. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart as the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The IRC reaction coordinate vs RMS gradient is the very useful. It shows that the the gradient had not yet reached zero and so a minimum on the PES had not been found. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the same energy to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm or disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is said to be more reliable than Approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:53:16Z

Da907: /* Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

The output file provides details such as those shown below which will enable the activation energy of the Cope rearrangement to be calculated later in this report.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2 method. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å for both distances. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart as the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The IRC reaction coordinate vs RMS gradient is the very useful. It shows that the the gradient had not yet reached zero and so a minimum on the PES had not been found. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the same energy to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm or disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:47:04Z

Da907: /* Optimising the 'Chair' and 'Boat' Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

The output file provides details such as those shown below which will enable the activation energy of the Cope rearrangement to be calculated later in this report.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2 method. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å for both distances. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart as the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:42:56Z

Da907: /* Vibrational Analysis */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

The output file provides details such as those shown below which will enable the activation energy of the Cope rearrangement to be calculated later in this report.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:40:53Z

Da907: /* Optimising the Reactants and Products */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower energy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. This suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set is unnecessary especially when one takes into account the increase time involved in calculations.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:30:44Z

Da907: /* Conclusion */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencies) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:30:07Z

Da907: /* References */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencsie) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

Rep:Mod:DAAO phys

2010-03-26T00:29:34Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)<ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

! Ea(0K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

!Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 <ref name="chem_wiki">[http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3</ref> / kcal/mol
! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencsie) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-26T00:26:54Z

Da907: /* Conclusions */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)/ kcal/mol

! Ea(0K) given in Appendix 1 / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

! Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 / kcal/mol

! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusion===
This report has focussed on the Cope rearrangement. The reactants and products with both an ‘anti’ or ‘gauche’ arrangement of the four central carbon atoms were optimised and discussed with regards to their strain and favourable interactions. It was found that the ''gauche3'' was the lowest energy conformer of 1,5-hexadiene despite its torsional strain and it was suggested that this was due to favourable interactions. Optimising at the low level of theory followed by a higher level has also been demonstrated throughout the report. It was seen that very slight changes in the geometry have large effects on the relative energy. Vibrational analysis was used to ensure that optimisation was successful considering that one would not expect any negative frequencies (imaginary frequencsie) for reactants or products but only for transition states. For the ‘chair’ transition structure this frequency was at -818 cm-1 while for the boat it was at -840 cm-1. The transition structures were optimised through a variety of methods including the frozen coordinate and the QST2 method. In order to ascertain which transition structure lead to which low energy conformer of 1,5-hexadiene, the IRC method was employed. The different approaches to achieve a minimum geometry from this method were also discussed. Suprisingly, it was found that Approach 1 was the most reliable and that the ‘chair’ and ‘boat’ transition structures lead to the ''gauche2'' and ''gauche3'' conformers of 1,5-hexadiene respectively. Finally the activation energies of the Cope rearrangement via the ‘chair’ and ‘boat’ transition structures were calculated with good agreement with the values given in Appendix 1. It was seen that the ‘chair’ transition structure has a lower activation energy and therefore it was suggested that the ''gauche2'' conformer is the kinetic product of the Cope rearrangement while ''gauche3'' is formed under thermodynamic conditions. Unfortunately due issues with the chemistry wiki during this computational module, the Diels Alder Cycloaddition section was not attempted.

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-26T00:00:59Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)/ kcal/mol

! Ea(0K) given in Appendix 1 / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

! Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 / kcal/mol

! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

As noted earlier there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T23:58:22Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)/ kcal/mol

! Ea(0K) given in Appendix 1 / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

! Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 / kcal/mol

! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

We can see that the calculated activation energies agree well with the experimental and appendix values. The activation energy at both 0 and 298.15K is smaller for the ‘chair’ TS than the ‘boat’ TS. This means that under kinetic conditions the cope rearrangement is more likely to proceed via the ‘chair’ TS leading to the ''gauche2'' conformer of 1,5-hexadiene. Whereas under thermodynamic control the ''gauche3'' conformer is more likely to form (as it is lower in energy) via the ‘boat’ transition structure.

From the above we can also see that there are only slight changes in the geometries of the structures obtained at different levels of theory (i.e. HF/3-21G and B3LYP/6-31G*).

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T23:38:16Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)/ kcal/mol

! Ea(0K) given in Appendix 1 / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

! Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 / kcal/mol

! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T23:37:11Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)/ kcal/mol

! Ea(0K) given in Appendix 1 / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

! Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(298.15K)/ kcal/mol

! Ea(298.15K) given in Appendix 1 / kcal/mol

! Difference between Calculated and Appendix 1 Ea (298.15K)/ kcal/mol

|-

|’Chair’ TS

|33.15

|33.17

|0.02

|-

|’Boat’ TS

|41.31

|41.32

|0.01

|}

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T23:34:34Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies for the reactions via both transition structures, one must first reoptimise both the 'chair' and 'boat' transtions strutures at the B3LYP/6-31G* level (and carry out frequency calculations). The appropriate section from the output files of the transition structures must then be compared to that of the ''anti2'' structure. The results are shown below in a table where Ea (0K) is the activation energy at 0K. This is calculated as the difference between the sum of electronic and zero-point energies of the ''anti2'' structure and each transition structure. Ea (298.15K) is the activation energy for the reaction at 298.15K. This is calculated as the difference between the sum of electronic and thermal energies of the ''anti2'' structure and each transition structure.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!Calculated Ea(0K)/ kcal/mol

!Experimental Ea(0K)/ kcal/mol

! Ea(0K) given in Appendix 1 / kcal/mol

!Difference between Calculated and Experimental Ea (0K)/ kcal/mol

! Difference between Calculated and Appendix 1 Ea (0K)/ kcal/mol

|-

|’Chair’ TS

|34.04

|33.5 ± 0.5

|31.06

|0.54 ± 0.5

|2.98

|-

|’Boat’ TS

|41.94

|44.7 ± 2.0

|41.96

|2.76 ± 2.0

|0.02

|}

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T22:46:37Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]
|[[Image: DAAO boat Ea output.png| 585 × 148 px]]
|[[Image:DAAO 1st anti reopt thermo.png| 585 × 148 px]]
|}

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T22:39:50Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|}

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T22:38:56Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-
|}

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T22:37:06Z

Da907: /* The Cope Rearrangement Tutorial */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336 {{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T22:36:19Z

Da907: /* References */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

===Conclusions===

===References===
<references/>

2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T22:35:17Z

Da907: /* Activation Energies for the Transition Structures */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

===Conclusions===

===References===
<references/>
2. http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3

Rep:Mod:DAAO phys

2010-03-25T22:29:34Z

Da907: /* Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat' transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
In this approach, the IRC was redone computing the force constants at every step rather than once. It showed to be a reliable method above.

[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

As we Approach 2, the structure obtained has CS symmetry and does not correspond to any of the structures given in Appendix 1. This is suprising as the IRC reaction coordinate vs RMS gradient showed that a minimum on the PES had been found. This suggests that maybe the wrong minimum was found. This result is disappointing as it now cannot be confirmed that the 'boat' transition structure leads to the ''gauche3'' conformer.

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T22:21:21Z

Da907: /* Approach 2: Restart IRC & Increase Number of Iterations */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
Again, the number of iterations was increased to 100. The following results were obtained.

[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

The struture obtained has CS symmetry and does not correspond to any of the structures in the table of Appendix 1. This is expected as the graph above shows that the RMS gradient had not reached zero and so the minimum on the PES had not been found. A higher number of iterations may have lead to the ''gauche3'' structure and therefore would confirm that the boat transition struture leads to the ''gauche3'' conformer as found above. This again highlights the issue of choosing the correct number of iterations.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T22:15:53Z

Da907: /* Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table. This suggests that the 'boat' transition structure leads to the ''gauche3'' conformer of 1,5-hexadiene.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T22:13:42Z

Da907: /* Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Structure obtained after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T22:12:15Z

Da907: /* Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. ''Gauche3'' is the lowest energy conformer in the table.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T22:05:46Z

Da907: /* Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

The RMS gradient did not reach zero. In order to achieve the geometry minimum 3 approaches discussed above were carried out for the 'boat transition structure.

=====Approach 1: Run a Normal Minimisation on Structure Obtained After 50 Iterations=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

The structure achieved has C1 symmetry and corresponds to the ''gauche3'' structure in the table in Appendix 1. Gauche3 is the lowest energy conformer in the table.

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T22:00:29Z

Da907: /* Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry obtained from ‘boat’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>Geometry obtained from Boat TS after 50 iterations</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:57:45Z

Da907: /* Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>Geometry after 50 iterations of Chair TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:54:52Z

Da907: /* Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>IRC (50 iterations) for ’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised using the QST2 method was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:53:56Z

Da907: /* Approach 3: Redo IRC Computing Force Constants at Every Step */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>IRC (50 iterations) for ’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

From the graphs above we can see that the RMS gradient reached zero and therefore the minimum geometry was obtained. As expected this approach yielded a structure which corresponds to ''gauche2''. It can now be said we condfidence that the 'chair' transition structure leads to the ''gauche2'' 1,5-hexadiene conformer. Just like the ''gauche2'' structure, this geometry has C2 symmetry and the energies agree to 5 decimal places.

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:49:06Z

Da907: /* Approach 2: Restart IRC & Increase Number of Iterations */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>IRC (50 iterations) for ’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained. The number of iterations was increased to 100 and the IRC was restarted. The results obtained are shown below.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

Even though it has been said that this approach is more reliable, we can see that after doubling the number of iterations the expected ''gauche2'' structure has not been obtained. This structure has C2h symmetry and corresponds to the ''anti3'' structure in the table in Appendix 1. From the graphs we can see that RMS gradient had not reached zero and so the minimum geometry was not achieved. This highlights a problem with this approach. Choosing the correct number of iterations can only be found through trial and error. Too few or too many iterations and the wrong geometry is obtained.

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:38:41Z

Da907: /* Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>IRC (50 iterations) for ’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. This also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:37:11Z

Da907: /* Approach 1: Run a Normal Minimisation */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>IRC (50 iterations) for ’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation on Struture Obtained After 50 Iterations=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. From this, we also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:35:26Z

Da907: /* Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry obtained using IRC method for ‘chair’ transition structure after 50 iterations<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>IRC (50 iterations) for ’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the ''gauche2'' structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that the structure obtained from the previous calculation was close to a local minimum. From this, we also suggests that the the ''gauche2'' conformer of 1,5-hexadiene is formed from the 'chair' transtion structure. We will now consider the other possible approaches to obtain a minimum geometry to see whether they confirm of disprove this suggestion.

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:27:35Z

Da907: /* Intrinsic Reaction Coordinate (IRC) Method */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
It is difficult to tell which conformer of 1,5-hexadiene is connected to the optimised transtion structures found above. The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached. The struture obtained did not correspond to any of the low energy conformers of 1,5-hexadiene given in Appendix 1.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

The structure obtained from this method has C2 symmetry and corresponds to the gauche2 structure in the table in Appendix 1 with the an energy correct to 5 decimal places. This suggests that

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:16:43Z

Da907: /* Optimising the 'Boat' Transition Structure */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

However, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:14:16Z

Da907: /* Optimising the 'Boat' Transition Structure */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. Using the ''anti2'' stucture previously optimised, it was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

Now, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:12:48Z

Da907: /* Optimising the 'Chair' Transition Structure */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. Both structures have a carbon-carbon bond length of 1.39 Å, a distance of 2.02 and 2.88 Å between the terminal and central carbons of the transition structure respectively. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. It was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

Now, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T21:07:32Z

Da907: /* Optimising the 'Chair' Transition Structure */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

The optimised structures from both methods have the same bond lengths and angles. The frozen coordinate method is more time consuming as it requires two calculations. However, this method yielded a slightly lower energy 'chair' transition structure by 2.1 x 10-7 a.u.

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. It was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

Now, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T20:58:12Z

Da907: /* Optimising the 'Chair' Transition Structure */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

After optimisation the distance between the terminal carbons decreased from 2.13 and 2.07 Å to 2.02 Å in both cases. The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure looks similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

The second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. It was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

Now, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T20:48:58Z

Da907: /* Optimising the Reactants and Products */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. Reoptimisation using a better basis set showed very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles. As there is such a small difference in bond lengths between the two optimised structures comparison to literature is futile. However, this small difference between the structure optimised at different levels of theory suggests that a smaller basis set sometimes is appropriate for calcualtions and a larger basis set especially when one takes into account the increase time involved in calculations is unnecessary.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure look similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

During the second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. It was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

Now, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T20:39:20Z

Da907: /* Optimising the Reactants and Products */

=Module 3: Transition States & Reactivity=

==Introduction==

This report cites and discusses the results from a set of computational experiments involving the Cope rearrangement. This includes characterising the transition structures on the potential energy surfaces of this rearrangement. This builds both on previous work performed during second year physical chemistry laboratory course at Imperial College London in 2009 and the more recent computational laboratory course in 2010. Here, using methods based on molecular orbitals, one will calculate what the transition structures of this rearrangement will look like as well as reaction paths and barrier heights.

==The Cope Rearrangement Tutorial==

This section focuses on the Cope rearrangement of 1,5-hexadiene in order to show how chemical reactivity problems can be studied. This will involve locating the low-energy minima and transition structures on the 1,5-hexadiene potential energy surface and hence determining the preferred reaction mechanism. After some controversy, it is generally believed that this [3,3]-sigamatropic shift rearrangement occurs via a concerted mechanism with either a ‘chair’ or ‘boat’ transition state. <ref name="DFT"> Wiest, O.; Black, K. A.; Houk, K. N., ''J. Am. Chem. Soc'', '''1994''', 116 (22), 10336{{DOI| 10.1021/ja00101a078}} </ref>

[[Image: DAAO cope mechanism.png|663 × 370px|thumb|center|Cope rearrangement]]

===Optimising the Reactants and Products===

Using the program GaussView 3.09, a molecule of 1,5-hexadiene was created so that its four central carbon atoms approximately had an anti-periplanar arrangement. This structure was tidied up by using the clean function. The structure was then optimised at the HF/3-21G level of theory. This means that the optimisation calculation using Gaussian was done using the the Hartree Fock method and the 3-21G basis set. The calculation summary did not show the point group of the structure and therefore was symmetrised which then showed the point group. This process was then repeated for 1,5-hexadiene with the four central carbon atoms in a gauche arrangement. These optimised structures were then compared to those given in a table in Appendix 1 and identified. The results obtained are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO react gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO React gauche1.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png|400 × 221 px]]
|[[Image:DAAO gauche calc summary.png|400 × 221 px]]
|-
| Point Group
|Ci
|C2
|-
|Structure in Appendix 1 Table
|''anti2''
|''gauche4''
|}

The above shows the anti conformer to be lower in energy. This could be due to there being less torsional strain present in the molecule. In order to achieve lower eneergy conformers, both the anti and gauche structures shown above were manipulated (by changing the dihedral angles) to reduce steric strain. These geometries were then optimised and indentified with reference to the table in Appendix 1. The results are shown below.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!Anti Conformer
!Gauche Conformer
|-
|Optimised Structure
|[[Image:DAAO React 2nd anti.jpg|400 × 221 px]]
|[[Image:DAAO React 2nd gauche.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React anti2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React gauche2 jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO 2nd anti calc summary.png|288 × 167 px]]
|[[Image:DAAO 2nd gauche calc summary.png|288 × 167 px]]
|-
|Point Group
|Ci
|C1
|-
|Structure in Appendix 1 Table
|''anti1''
|''gauche5''
|}

From the above we can see that manipulating the anti conformer lead to a lower energy geomtery yet in the case of the gauche isomer manipulation lead to a higher energy conformer. Thes suggests the possiblity that there is a favorable interaction present involving the carbon-carbon double bond and the vincinal proton in the gauche conformer that perhaps compensates for the additional torsional strain compared to the anti isomer.

All of the structures drawn agree with the values given in Appendix 1 to 5 decimal places.

The anti 1,5-hexadiene with Ci symmetry was then reoptimised at the higher level of theory of B3LYP/6-31G*.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!
!HF/3-21G
!B3LYP/6-31G*
|-
|Optimised Structure
|[[Image:DAAO react anti.jpg|400 × 221 px]]
|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO react anti.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO anti calc summary.png]]
|[[Image:DAAO 1st anti reopt calc summary.png]]
|-
| Point Group
|Ci
|Ci
|}

Comparing the different levels of theory used for the optimisation the following was noted:

[[Image:React anti1 labelled.jpg| 800 × 442 px|center|thumb|''Anti2'' structure obtained from HF/3-21G optimisation]]

[[Image:DAAO React 1st anti reopt labelled.jpg|800 × 442 px|center|thumb|''Anti2'' structure obtained from B3LYP/6-31G* optimisation]]

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Bond
!HF/3-21G Optimised Structure Bond Distance/ Å
!B3LYP/6-31G* Optimised Structure Bond Distance/ Å
!Difference in Bond Distances between Methods/ Å
|-
|C1=C2
|1.32
|1.33
|0.01
|-
|C2-C6
|1.51
|1.50
|0.01
|-
|C6-C9
|1.55
|1.55
|0.0
|-
| C9-C12
|1.51
|1.50
|0.01
|-
|C12=C13
|1.32
|1.33
|0.01
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
!Dihedral Angle
!HF/3-21G Optimised Structure Dihedral Angle/ ⁰
! B3LYP/6-31G* Optimised Structure Dihedral Angle/ ⁰
! Difference in Dihedral Angle between Methods/ ⁰
|-
|C1-C2-C6-C9
|115
|119
|4
|-
| C2-C6-C9-C12
|180
|113
|67
|-
| C6-C9-C12-C13
|115
|119
|4
|}

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
! Angle
!HF/3-21G Optimised Structure Angle/ ⁰
!B3LYP/6-31G* Optimised Structure Angle/ ⁰
!Difference in Angle between Methods/ ⁰
|-
|C1-C2-C6
|125
|125
|0
|-
| C2-C6-C9
|111
|113
|2
|-
| C6-C9-C12
|111
|113
|2
|-
| C9-C12-13
|125
|125
|0
|}

Energies obtained between the methods cannot be compared as different basis sets were used. There is very little difference in bond lengths between the two structures. Bond lengths are either identical or slightly longer for the structure optimised to a higher level of theory. The greatest difference in geometry between the two optimised structures is found when one looks at their dihedral angles.

===Vibrational Analysis===

It can be confirmed that the B3LYP/6-31G* optimisation was successful by vibrational analysis. Frequency calculations were performed using the same method and basis set as used for the optimisation (B3LYP/6-31G*).

[[Image:DAAO 1st anti reopt freq.png|297 × 230 px|thumb|center|Calculation summary for the ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO anti reopt IR.png|574 × 322 px|thumb|center|IR spectrum of ''anti2'' structure from the B3LYP/6-31G* level of theory]]

[[Image:DAAO 1st anti reopt freq output.png|592 × 235 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

There are no imaginary frequencies i.e. all vibrational frequencies are positive so it is known that optimisation was successful and a transition structure was not achieved.

Looking at the output file for the frequency calculation one can learn about the thermochemistry which can then be compared to experimental values.

[[Image:DAAO 1st anti reopt thermo.png|582 × 146 px|thumb|center|Excerpt of output file for ''anti2'' structure from the B3LYP/6-31G* level of theory]]

==Optimising the 'Chair' and 'Boat' Transition Structures==
Here, both the ‘chair’ and ‘boat’ transition structures will be optimised by computing the force constants at the beginning of the calculation, using the redundant coordinate editor and QST2. The reaction coordinate will be visualised, the IRC run and the activation energies for the Cope rearrangement by both the ‘chair and ‘boat transition structures.

===Optimising an Allyl Fragment===
An allyl fragment (CH2CHCH2) was created using GaussView 3.09 and optimised at the HF/3-21G level of theory.

{|border="1" cellpadding="5" cellspacing="0" align="center"
|-
|Optimised Structure
|[[Image:DAAO Allyl opted.jpg|400×221px]]
|-
|jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>CH2CHCH2 opt jmol.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>
|-
|Calculation Summary
|[[Image:DAAO allyl opt calc summary.png|290 × 169px]]
|}

[[Image:DAAO allyl converged output.png|461 × 142px|thumb|center|Excerpt of output file for the optimised output file]]

===Optimising the 'Chair' Transition Structure===

Two of these fragments were oriented at shown below and optimised with Gaussian by selecting Opt+Freq as the job type, ‘Optimisation to a TS (Berny)’, force constants to be calculated once, and HF/3-21G as the level of theory. The keywords Opt=NoEigen were also added to prevent the calculation from crashing.

[[Image:Chair guess starting.png|400 × 221px|thumb|center|'Chair' transition structure starting orientation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO allyl starting.mol</uploadedFileContents>
<text>Starting Geometry</text>
</jmolAppletButton>
</jmol>]]

[[Image:DAAO Chair opt berny.jpg|400 × 221px|thumb|center|’Chair’ transition structure after optimisation <jmol>
<jmolAppletButton>
<uploadedFileContents>DAAO Chair opt berny.mol</uploadedFileContents>
<text>Optimised Geometry</text>
</jmolAppletButton>
</jmol>]]

The job was successful as vibrational analysis shows that an imaginary frequency of -818 cm-1 was obtained. This vibrational mode corresponds to the Cope rearrangement and shows two terminal carbon atoms approach each other to form a bond while the opposite two carbons atoms move apart when the C-C bond breaks.

[[Image:DAAO chair berny freq calc summary.png|289 × 166px|thumb|center|Calculation summary for the optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:DAAO berny chair IR.png|1000 × 106px|thumb|center|IR spectrum for the ‘chair’ transition structure optimised after optimisation of the ‘chair’ transition structure to a TS (Berny)]]

[[Image:Chair opt berny -818.jpg|400 × 221px|thumb|center|Screenshot of vibration at - 818 cm-1]]

The guess ‘chair’ transition structure was then optimised using the frozen coordinate method. This was done in two steps the first of which involved fixing the distance between the terminal carbons forming/ breaking a bond during the rearrangement to 2.2 Å and using Gaussian to perform the optimisation.

[[Image:DAAO chair ts c.png|293 × 166 px|thumb|center|Calculation Summary for step 1 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image:Chair ts c 2 20.jpg|400 × 221px|thumb|center|Step 1 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is fixed to 2.2 Å<jmol>
<jmolAppletButton>
<uploadedFileContents>Chair ts c 2 20.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.2 angstroms</text>
</jmolAppletButton>
</jmol>]]

This optimised structure look similar to that achieved after optimisation to a TS (Berny) but the C-C bond length is 2.2 Å rather than 2.02 Å.

During the second step of this optimisation method involved optimising to a TS (Berny) again but this time the force constants were not calculated.

[[Image: DAAO chair ts d calc summary.png|293 × 166 px|thumb|center|Calculation Summary for step 2 of the optimisation of the ‘chair’ transition structure by the frozen coordinate method]]

[[Image: Chair ts d 2 02.jpg|400 × 221px|thumb|center|Step 2 of optimisation of the ‘chair’ transition structure by the frozen coordinate method. C-C bond length is now to 2.02 Å <jmol>
<jmolAppletButton>
<uploadedFileContents> DAAO Chair ts d 2 02.mol</uploadedFileContents>
<text>Optimised TS C-C = 2.02 angstroms</text>
</jmolAppletButton>
</jmol>]]

===Optimising the 'Boat' Transition Structure===
The ‘boat’ transition structure was then optimised using the QST2 method. The method involves both the reactants and products and tries to interpolate the two to find the transition structure. It was first necessary to ensure that the reactants and products were labelled in the same way.

[[Image:Boat opt react fail.jpg|400 × 221px|thumb|center|Reactant labelled]]

[[Image:Boat opt product fail.jpg|400 × 221px|thumb|center|Product labelled]]

After submitting the ‘Opt+Freq’ job to Gaussian selecting TS(QST2) and the same method and basis set as previously used it was seen that the job had failed. This is due to the possible rotation about the central bonds not being considered. From this, we know that the QST2 method will not locate the transition structure starting from the above structures for the reactant and product.

Now, by using the original input file and modifying the reactant and product starting configurations one can locate the boat transitions structure.

[[Image:Qst2 rearranged react.jpg|400 × 221px|thumb|center|Modified reactant starting configuration with labels]]

[[Image:Qst2 rearranged prod.jpg|400 × 221px|thumb|center|Modified product starting configuration with labels]]

[[Image: DAAO rearranged calc summary.png|400 × 221px|thumb|center|Calculation summary for the optimisation of the ‘boat’ transition structure using the QST2 method]]

[[Image: Rearranged ts.jpg|400 × 221px|thumb|center|Optimised ‘boat’ transition structure obtained from the QST2 method<jmol>

<jmolAppletButton>

<uploadedFileContents> QST2 rearranged ts.mol</uploadedFileContents>

<text>Optimised TS</text>

</jmolAppletButton>

</jmol>]]

Looking the output file, it can be seen that there is one imaginary frequency at -840 cm-1. This confirms that a transition state was obtained. This corresponds to the cope rearrangement via the ‘boat’ transition structure.

[[Image:DAAO boat ts IR.png|1000 × 100px|thumb|center|IR spectrum of the ‘boat’ transition structure]]

[[Image: DAAO boat ts output.png|400 × 221px|thumb|center|Excerpt of output file]]

[[Image: DAAO boat ts 840 vib.png|400x221px|thumb|center|Vibration at -840 cm-1]]

===Intrinsic Reaction Coordinate (IRC) Method===
The Intrinsic Reaction Coordinate (IRC) method allows us to predict which conformer of 1,5-hexadiene will be obtained from the ‘chair’ and ‘boat’ transition structures. Gaussian is used in this method and enables us to follow the minimum energy path with small changes in the geometry in the direction where the gradient of the potential energy surface is steepest.

====Intrinsic Reaction Coordinate (IRC) Method for 'Chair' Transition State====
The checkpoint file for the chair structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC 50 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed.

=====Approach 1: Run a Normal Minimisation=====

This approach is the fastest of the three suggested however, it can lead to obtaining the wrong minimum if the geometry is not close enough to a local minimum. The following results were obtained.

[[Image: DAAO IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO IRC app1 converged.png|452x139px|thumb|center|Excerpt of output file for approach 1]]

[[Image: IRC approach1.jpg|400x201px|thumb|center|Geometry after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach1 jmol.mol</uploadedFileContents>

<text>Approach 1</text>

</jmolAppletButton>

</jmol>]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====

This approach is more reliable than approach 1 but if too many points are used the wrong geometry can be obtained.

[[Image: DAAO IRC app2 calc summary.png|400x201px|thumb|right|Calculation summary for approach 2 (100 iterations)]]

[[Image: IRC approach2.jpg|400x201px|thumb|left|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====

This approach is said to be the most reliable but it is not suitable for large systems and is expensive.

[[Image:DAAO IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: IRC approach3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> IRC approach3 jmol.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

====Intrinsic Reaction Coordinate (IRC) Method for 'Boat' Transition State====
The checkpoint file for the boat structure optimised to a TS (Berny) was opened. Using Gaussian, the job type IRC was chosen with the reaction coordinate computed only in the forward direction as it is symmetrical. The force constant was calculated once, IRCMax option was left unchecked and the number of points along the IRC was increased from the default 6 to 50.

After the job had finished, it was seen from the following that a minimum geometry was not reached.

[[Image: DAAO Boat IRC 50 calc summary.png|400x201px|thumb|left|Calculation summary for IRC method (50 iterations)]]

[[Image: Boat IRC 50.jpg|400x201px|thumb|right|Geometry of ‘chair’ transition structure after 50 iterations using the IRC method<jmol>

<jmolAppletButton>

<uploadedFileContents> Boat IRC 50.mol</uploadedFileContents>

<text>’Chair’ TS</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO Boat IRC 50 graphs.png|800x459px|thumb|center|Graphs showing total energy and RMS gradient vs IRC reaction coordinate after 50 iterations using the IRC method]]

In order to achieve the geometry minimum 3 options were suggested. Each approach will now be discussed again.

=====Approach 1: Run a Normal Minimisation=====

[[Image: DAAO boat IRC app1 calc summary.png|400x201px|thumb|center|Calculation summary for approach 1]]

[[Image: DAAO boat IRC app1.jpg|400x201px|thumb|center|Geometry of ‘chair’ transition structure after approach 1<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app1.mol</uploadedFileContents>

<text>Approach 1 </text>

</jmolAppletButton>

</jmol>]]

[[Image:DAAO boat app1 converged.png|439 × 139px|thumb|center|Excerpt of output file for approach 1]]

=====Approach 2: Restart IRC & Increase Number of Iterations=====
[[Image: DAAO boat IRC app2 calc summary.png|400x201px|thumb|left|Calculation summary for approach 2 (100 iterations)]]

[[Image:DAAO boat IRC app2.jpg|400x201px|thumb|right|Geometry after approach 2<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app2.mol</uploadedFileContents>

<text>Approach 2</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app2 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after 100 iterations using the IRC method]]

=====Approach 3: Redo IRC Computing Force Constants at Every Step=====
[[Image: DAAO boat IRC app3 calc summary.png|400x201px|thumb|left|Calculation summary for approach 3]]

[[Image: DAAO boat IRC app3.jpg|400x201px|thumb|right|Geometry after approach 3<jmol>

<jmolAppletButton>

<uploadedFileContents> DAAO boat IRC app3.mol</uploadedFileContents>

<text>Approach 3</text>

</jmolAppletButton>

</jmol>]]

[[Image: DAAO boat IRC app3 graphs.png|800x459px|thumb|center|Graphs showing IRC reaction coordinate vs total energy and RMS gradient after approach 3]]

===Activation Energies for the Transition Structures===
In order to calculate the activation energies of the transitions structures both structures were reoptimised at the B3LYP/6-31G* level and frequency calculations were carried out.

{|border="1" cellpadding="5" cellspacing="0" align="center"

|-

!

!’Chair’

!’Boat’

!Anti2

|-

|Optimised Structure

|[[Image: DAAO chair reopt.jpg|400x221px]]

|[[Image: DAAO boat reopt.jpg|400x221px]]

|[[Image:DAAO React 1st anti reopt.jpg|400 × 221 px]]

|-

|jmol

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO chair reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>DAAO boat reopt.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|<jmol>

<jmolAppletButton>

<uploadedFileContents>React 1st anti reopt jmol.mol</uploadedFileContents>

<text>Optimised Geometry</text>

</jmolAppletButton>

</jmol>

|-

|Calculation Summary

|[[Image: DAAO chair Ea calc summary.png|400x201px]]

|[[Image: DAAO boat Ea calc summary.png|400x201px]]

|[[Image: DAAO 1st anti reopt calc summary.png|400x201px]]

|-

| Point Group

|C2h

|C2v

|Ci

|-

| IR Spectrum

|[[Image: DAAO chair Ea IR.png|400x201px]]

|[[Image: DAAO boat Ea IR.png|400x201px]]

|[[Image:DAAO anti reopt IR.png|400x201px]]

|-

|Imaginary Frequency/ cm-1

| -567

| -531

|n/a

|-

|Image of Imaginary Frequency

|[[Image: DAAO chair Ea vib.png |400x201px]]

|[[Image: DAAO boat Ea vib.png|400x201px]]

| n/a

|-

|Excerpt of output file regarding Thermochemistry

|[[Image: DAAO chair Ea output.png | 585 × 148 px]]

|[[Image: DAAO boat Ea output.png| 585 × 148 px]]

|[[Image: | 585 × 148 px]]

|}

Rep:Mod:DAAO phys

2010-03-25T20:31:43Z

Da907: /* Optimising the Reactants and Products */

Rep:Mod:DAAO phys

2010-03-25T20:24:44Z

Da907: /* Optimising the Reactants and Products */