File:Shane exo guessx.mol

2010-12-18T21:03:14Z

So208:

File:Shane endo opt.out

2010-12-18T20:18:50Z

So208:

Rep:Mod:shaneomar3

2010-12-18T20:06:55Z

So208:

=Module 3=

==The Cope Rearrangement==

The Cope rearrangement of 1,5-hexadiene, which is a [3,3]-sigmatropic shift, will be investigated in order to understand how to carry out a chemical reactivity problem in Gaussview. This will be carried out by looking for the low energy minima of the structure and then the transition state, which yields information about the preferred reaction mechanism.

===Optimising the reactants and products===
[[Image:shane_anti_opt.gif|right|thumb|Summary of anti optimisation]]

A molecule of 1,5-hexadiene with an "anti" linkage was built and cleaned in Gaussview before being optimized at the HF/3-21G level of theory. The result of this optimisation is shown on the right. The point group was found to be '''C<sub>2</sub>'''.

<jmol><jmolApplet><title>Anti hexadiene optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>shane_anti_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

[[Image:shane_gauche_opt.gif|right|thumb|Summary of gauche optimisation]]

Next, a molecule of 1,5-hexadiene with a "gauche" linkage for the central four C atoms was built and optimised in the same way. The result is shown on the right, the point group was also '''C<sub>2</sub>'''.

<jmol><jmolApplet><title>Gauche hexadiene optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>shane_gauche_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

This gauche structure might be expected to be higher in energy than the anti (above), due to steric repulsion between -C=C groups. The results do indeed show that this gauche conformation is lower in energy by '''0.67 kcal/mol'''. However, the distance between the -C=C groups is not small, so repulsion may not be an issue. There may be other electronic interactions which can explain the relative stability of these structures, which will be further explored.

[[Image:shane_gauche3_opt.gif|right|thumb|Summary of gauche3 optimisation]]

One such stabilising interaction could be between the vinyl C-H and the other Pi bond, so called CH/Pi interaction<ref name="ja00111a016"> Study of 1,5-hexadiene - {{DOI|10.1021/ja00111a016}}</ref>. This interaction would be possible in the gauche structure optimised below (note the proximity of the vinyl H to the other C=C). The results of this optimisation are shown on the right.

<jmol><jmolApplet><title>Gauche3 hexadiene optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>shane_gauche3_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The results show that this is the lowest energy structure, which suggests the hypothesis was correct. On comparison with the table in 'Appendix 1', the structures optimised here can be identified as '''anti1''', '''gauche4''' and '''gauche3''' respectively.

[[Image:shane_anti2_opt.gif|right|thumb|Summary of anti2 optimisation]]

The Ci anti2 conformation of 1,5-hexadiene was then built and optimised using the HF/3-21G level of theory. The results are shown on the right, the optimised molecule below.

<jmol><jmolApplet><title>Anti2 hexadiene optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>shane_anti2_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

This structure has the same energy and symmetry ('''Ci''' point group) as the one given in the table and. Next, a higher level of optimisation was carried out: DFT/B3LYP, followed by a frequency analysis to check that the energy was a minimum. The results of the vibrational analysis showed that they were all positive and real, confirming the minimum. The lowest energy vibration is displayed below.

[[Image:shane_anti2_reopt.gif|right|thumb|Summary of anti2 reoptimisation]]

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>zoom 100;frame 3;vectors 4;vectors scale 5.0;color vectors red; vibration 3;
</script><uploadedFileContents>shane_anti2_freq.out</uploadedFileContents>
</jmolApplet>
</jmol>

Sum of electronic and zero-point Energies= -234.469203 au

Sum of electronic and thermal Energies= -234.461856 au

Sum of electronic and thermal Enthalpies= -234.460911 au

Sum of electronic and thermal Free Energies= -234.500782 au

These values are identical to those give in the appendix which shows a good agreement.

===Optimising the "chair" and "boat" transition structures===

In order to calculate the activation energies for the cope rearrangement, the two possible transition structures were optimised in different ways. Both of these chair and boat transition structures consist of two allyl fragments and the structures were optimised using the following methods.

[[Image:shane_chair_ts_opt1.gif|right|thumb|Summary of chair TS optimisation]]

First, the '''chair''' TS structure was built in Gaussview by optimising the fragment at the HF/3-21G level of theory and placing the terminal ends of the allyl fragments roughly 2.2 Å apart. This "guess" structure was then optimised to a transition state (TS Berny). The reults of this optimisation are shown, with the imaginary vibration corresponding to the cope rearrangement shown below.

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>zoom 100;frame 37;vectors 4;vectors scale 5.0;color vectors red; vibration 3;
</script><uploadedFileContents>shane_chair_ts_opt1.out</uploadedFileContents>
</jmolApplet>
</jmol>

[[Image:shane_chair_ts_opt2.gif|right|thumb|Frozen bond optimisation]]

Next, the chair structure was optimised again using the frozen orbital method. Using the Redundant Coor Eidtor, the bonds between the two allyl groups were frozen at 2.2 Å. This structure was then optimised to a minimum, the results and structure are shown.

<jmol>
<jmolAppletButton>
<uploadedFileContents>shane_chair_ts_opt2.mol</uploadedFileContents>
<text>Chair transition state with frozen bonds</text>
<script>select atomno=6,atomno=11;measure 6 11</script>
</jmolAppletButton>
</jmol>

[[Image:shane_chair_ts_opt3.gif|right|thumb|Hessian modified optimisation]]

These bonds which are forming/breaking were then optimised (Hessian modified) without calculating the force constant. The resulting structure and summary are given below.

<jmol>
<jmolAppletButton>
<uploadedFileContents>shane_chair_ts_opt3.mol</uploadedFileContents>
<text>Hessian modified chair TS structure</text>
<script>select atomno=6,atomno=11;measure 6 11</script>
</jmolAppletButton>
</jmol>

As the structures in the Jmol buttons show, the bond length (making/breaking) is '''2.02 Å''' in the Hessian modified structure. This is 0.18 Å shorter than the frozen bond optimisation.

The boat transition structure was then optimised, firstly using the QST2 calculation. This involves building the reactant and product structures, and interpolating between the two to find the transition structure. The first attempt at this resulted in an error. The resulting clearly shows abnormal bonding as shown below:

<jmol><jmolApplet><title>First attempt boat optimisation</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>shane_boat_ts_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The cause of this error was due to the initial geometry used for the optimisation. In the QST2 method the reactant and product must be built to more closely resemble the transition structure in order for the calculation to work. The structures were rebuilt to more closely resemble a boat conformation, and the calculation repeated. This time the results were more reasonable, only one imaginary frequency was found. This represents the formation/breaking of the bonds and is shown below:
[[Image:shane_boat_ts_opt2.gif|right|thumb|Boat optimisation QST2]]

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>zoom 100;frame 51;vectors 4;vectors scale 5.0;color vectors red; vibration 3;
</script><uploadedFileContents>shane_boat_ts_opt2.out</uploadedFileContents>
</jmolApplet>
</jmol>

In order to determine the conformer of 1,5-hexadiene that is involved in the cope rearrangemnt, an Intrinsic Reaction Coordinate method was used. This allows you to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface. 50 points were visualised in this calculation, but the last point caused the energy to increase so was not used. Instead, the last point on the IRC was taken and a normal minimization was run on it. The results of this are shown:

[[Image:shane_irc.gif|right|thumb|Chair IRC]]
<jmol><jmolApplet><title>Optimised Chair from IRC</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>shane_chair_irc_opt.mol</uploadedFileContents>
</jmolApplet></jmol>

The energy and symmetry of this structure is a good match to the '''gauche2''' structure in the appendix. This would suggest that the reaction paths from the transitions structures will lead to a gauche2 structure. This is quite surprising because there are lower energy conformers of 1,5-hexadiene. However, the gauche2 structure seems to be closest in energy to the transition structure.

Next, the chair and boat transition structures were optimised at the B3LYP/6-31G(d) level of theory, followed by frequency calculations with the same method. The purpose of this was to find the activation energies by looking at thermochemistry data.

[[Image:shane_chair_freq.gif|left|thumb|Chair B3LYP/6-31G(d)]][[Image:shane_boat_freq.gif|right|thumb|Boat B3LYP/6-31G(d)]]

The geometry of the reactants and transition states optimised at the higher level are very close to those at the lower level of theory. The activation energies were calculated at 298.15<sup>o</sup>K by assuming the gauche2 conformer is the one which proceeds the rearrangement in both chair and boat pathways. The energy difference (looking at 'sum of electronic and thermal energy') between reactant and transition state was used to find the activation energy.

The activation energies calculated at the lower level of theory were significantly larger than the activation energies using higher level of theory. Using HF/3-21G, the ΔE (Chair) was '''44.21 kcal/mol''' and ΔE (Boat) was '''54.29 kcal/mol'''. Whereas with B3LYP/6-31G(d), ΔE (Chair) was '''32.60 kcal/mol''' and ΔE (Boat) was '''40.76 kcal/mol'''.

These values show that the cope rearrangement is more likely to occur via the chair transition state, which is not surprising since it is the lower energy conformer. The values are a good match to those in the appendix, and the activation energies calculated a 0<sup>o</sup>K are slightly lower than experimental values.

==The Diels Alder Cycloaddition==

[[Image:mb_da1.jpg |right|thumb|Diels Alder cycloaddition]]
The Diels Alder reaction is a type of pericylcic reaction. The HOMO/LUMO of one reactant reacts with the HOMO/LUMO of the other, which is only allowed if the symmetry of the orbitals is suitable for them to interact. To investigate this type of reaction the transition states can be built and analysed to understand the MO and bond formation of the reaction.

===Ethylene + Cis Cyclobutadiene===

[[Image:shane_butadiene_mo.jpg|left|thumb|HOMO of cis-butadiene]][[Image:shane_butadiene_mo2.jpg|right|thumb|LUMO of cis-butadiene]]
Cis-butadiene was built and optimised in gaussview using the AM1 semi-emperical molecular orbital method. The HOMO and LUMO were plotted and are displayed below.

These molecular orbitals can be classified as being either symmetric '''s''', or antisymmetric '''a''' with respect to the plane of symmetry going though the middle of the molecule perpendicularly. For example, the HOMO of cis-butadiene is anti-symmetric and the LUMO is symmetric. The HOMO and LUMO of ethylene are the Pi and Pi* orbitals, which are '''s''' and '''a''' respectively. Therefore you would expect the HOMO and LUMO pairs to interaction in the Diels Alder reaction because the symmetries are suitable.

[[Image:shane_prototype_homo.jpg|left|thumb|HOMO of transition state ('''a''')]][[Image:shane_prototype_lumo.jpg|right|thumb|LUMO of transition state ('''s''')]]

The transition state structure of the reaction was built and optimised using the same method as above. The partly formed C-C bonds were estimated as 1.6 Å in this optimisation. The MOs were plotted and are displayed on either side. The HOMO is antisymmetric and the LUMO is symmetric. This shows that the HOMO of the transition state was made from the overlap/interaction of the butadiene LUMO and ethylene HOMO. The LUMO transition state was made from the butadiene HOMO and ethylene LUMO. The orbitals are visually a good match to this description and also the symmetric and antisymmetric pair theory.

The geometry of the transition state can be viewed here:
<jmol>
<jmolAppletButton>
<uploadedFileContents>shane_prototype_opt.mol</uploadedFileContents>
<text>butadiene + ethylene TS structure</text>
<script>select atomno=1,atomno=11,atomno=4,atomno=14;measure 1 11;measure 4 14</script>
</jmolAppletButton>
</jmol>

The length of the partly formed C-C bonds is 2.12 Å (as shown in the Jmol Button). Typical sp<sup>3</sup>C - sp<sup>3</sup>C bond length is 1.54 Å, and sp<sup>2</sup>C - sp<sup>2</sup> bond length is 1.47 Å, so the partly formed bonds in this TS are much longer than a formed C-C bond. However, the Van der Waals radius of a carbon atom is 1.7 Å, which shows that there is definitely a bond being formed since the sum of the carbons' radii is 3.4 Å.

{| border="1"
|+ TS vibrations
! scope="col" | Imaginary frequency
! scope="col" | Lowest real frequency
|-
! scope="row" | <jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>zoom 100;frame 69;vectors 3;vectors scale 4.0;color vectors red; vibration 3;
</script><uploadedFileContents>shane_prototype_opt.out</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>200</size>
<script>zoom 100;frame 70;vectors 3;vectors scale 4.0;color vectors red; vibration 3;
</script><uploadedFileContents>shane_prototype_opt.out</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}

The vibration that corresponds to reaction path at the transition state is displayed above. The formation of the two bonds is synchronous, whereas the lowest positive frequency is an asynchronous vibration.

===Cyclohexadiene + Maleic Anhydride===

Cyclohexa-1,3-diene reacts with maleic anhydride to give primarily the endo adduct. The reaction is thought to be kinetically controlled so that the exo transition state should be higher in energy.

The exo and endo transition states were built in gaussview with a guess of 2.1 Å for the partly formed bond distances. The structures were optimised using the semi empirical/AM1 method and the geometries are shown below:

{| border="1"
|+ Endo and Exo TS geometries
! scope="col" |
! scope="col" | Exo TS
! scope="col" | Endo TS
|-
! scope="row" |
| <jmol>
<jmolApplet>
<uploadedFileContents>shane_exo_opt.mol</uploadedFileContents>
<script>select atomno=1,atomno=11,atomno=4,atomno=14;measure 1 11;measure 4 14</script>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<uploadedFileContents>shane_exo_opt.mol</uploadedFileContents>
<script>select atomno=1,atomno=11,atomno=4,atomno=14;measure 1 11;measure 4 14</script>
</jmolApplet>
</jmol>
|-
! scope="row" | Energy

| '''-0.00699434 hartree'''
| '''-0.00699435 hartree'''

|-
|}

===References===

<references />

File:Shane exo opt.mol

2010-12-18T19:41:25Z

So208:

2010-12-18T15:45:18Z

So208:

Rep:Mod:shaneomar3

2010-12-18T15:36:49Z

So208: