ChemWiki - User contributions [en]

Rep:Mod:pm08inorg2

2011-04-01T09:34:27Z

Pm08:

== Catalytic Polymerisation of Ethylene ==

===NiBr<sub>2</sub>(α-diimine)===
Most similar crystal structure reported shows dimerisation across two Ni centres, via bridging Br. Tetrahedral coordinaion at Ni.

<jmol>
<jmolApplet>
<title>Nicat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>NiBr2diimine.mol</uploadedFileContents>
</jmolApplet>
<jmolApplet>
<title>Nicat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>FIKPUL.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===FeCl<sub>2</sub>bis(imino)pyridine===
Distorted Square Based Pyramid at Fe.

<jmol>
<jmolApplet>
<title>Fecat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>FeCl2bisiminopyridine.mol</uploadedFileContents>
</jmolApplet>
</jmol>

File:FIKPUL.mol

2011-04-01T09:34:06Z

Pm08:

Rep:Mod:pm08inorg2

2011-04-01T09:33:52Z

Pm08:

== Catalytic Polymerisation of Ethylene ==

===NiBr<sub>2</sub>(α-diimine)===
Most similar crystal structure reported shows dimerisation across two Ni centres, via bridging Br. Tetrahedral coordinaion at Ni.

<jmol>
<jmolApplet>
<title>Nicat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>NiBr2diimine.mol</uploadedFileContents>
</jmolApplet>
<jmolApplet>
<title>Nicat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>FIKPUK.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===FeCl<sub>2</sub>bis(imino)pyridine===
Distorted Square Based Pyramid at Fe.

<jmol>
<jmolApplet>
<title>Fecat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>FeCl2bisiminopyridine.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Rep:Mod:pm08inorg2

2011-03-29T17:03:15Z

Pm08:

== Catalytic Polymerisation of Ethylene ==

===NiBr<sub>2</sub>(α-diimine)===
Most similar crystal structure reported shows dimerisation across two Ni centres, via bridging Br. Tetrahedral coordinaion at Ni.

<jmol>
<jmolApplet>
<title>Nicat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>NiBr2diimine.mol</uploadedFileContents>
</jmolApplet>
</jmol>

===FeCl<sub>2</sub>bis(imino)pyridine===
Distorted Square Based Pyramid at Fe.

<jmol>
<jmolApplet>
<title>Fecat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>FeCl2bisiminopyridine.mol</uploadedFileContents>
</jmolApplet>
</jmol>

File:FeCl2bisiminopyridine.mol

2011-03-29T16:58:06Z

Pm08:

Rep:Mod:pm08inorg2

2011-03-29T16:57:38Z

Pm08:

== Catalytic Polymerisation of Ethylene ==

<table>
<tr>
<td>
===NiBr<sub>2</sub>(α-diimine)===
Most similar crystal structure reported shows dimerisation across two Ni centres, via bridging Br:
</td>
<td>
<jmol>
<jmolApplet>
<title>Nicat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>NiBr2diimine.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td>
===FeCl<sub>2</sub>bis(imino)pyridine===
</td>
<td>
<jmol>
<jmolApplet>
<title>Fecat</title>
<color>white</color>
<size>500</size>
<script>rotate;</script>
<uploadedFileContents>FeCl2bisiminopyridine.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

File:NiBr2diimine.mol

2011-03-29T16:53:46Z

Pm08:

Rep:Mod:pm08inorg2

2011-03-29T16:53:14Z

Pm08: New page: == Catalytic Polymerisation of Ethylene == ===NiBr2(a-diimine)=== Most similar crystal structure reported shows dimerisation across two Ni centres, via bridging Br: <jmol> <jmolApplet> ...

== Catalytic Polymerisation of Ethylene ==

===NiBr2(a-diimine)===
Most similar crystal structure reported shows dimerisation across two Ni centres, via bridging Br:

<jmol>
<jmolApplet>
<title>Endo-Dicyclopentadiene</title>
<color>white</color>
<size>250</size>
<script>rotate;</script>
<uploadedFileContents>NiBr2diimine.mol</uploadedFileContents>
</jmolApplet>
</jmol>

Rep:Mod:pm08inorg4

2011-03-14T10:21:24Z

Pm08:

== Experiment 4 - Fluxional Process of the [B<sub>3</sub>H<sub>8</sub>]<sup>-</sup> Anion ==

The ground state geometry of the [B<sub>3</sub>H<sub>8</sub>]<sup>-</sup> anion was modelled, and the resulting geometry shown below, left. Using a QST2 type calculation, the TS of the fluxional process proposed, by rotation of one BH<sub>3</sub> unit was calculated, and optimised. The vibration along the reaction coordinate is shown, as well as a static TS structure. Notice the BH<sub>3</sub> unit has undergone a half rotation.
<table>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Arachno Borane Ground State Optimised</title><color>white</color><size>250</size>
<script>rotate;</script>
<uploadedFileContents>ArachnoB3H8GS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
Ground State
</td>
<td>
<jmol>
<jmolApplet>
<title>Arachno Borane Fluxional Transition State Optimised</title><color>white</color><size>250</size>
<script>frame 17;vectors 3;vectors scale 1;color vectors blue; vibration 2;</script><uploadedFileContents>aracnhoB3H8FluxTS.out</uploadedFileContents>
</jmolApplet>
</jmol>
Transition State Vibration
</td>
<td>

<jmol>
<jmolApplet>
<title>Arachno Borane Fluxional Transition State Optimised</title><color>white</color><size>250</size>
<script>rotate;</script>
<uploadedFileContents>aracnhoB3H8FluxTS.out</uploadedFileContents>
</jmolApplet>
</jmol>
Transition State Static
</td>
</tr>
</table>
The log files of these two calculations are available here:

Ground State: [http://hdl.handle.net/10042/to-7644]

Transition State: [http://hdl.handle.net/10042/to-7645]

Calculation to the DFT B3LYP 6-31G(d,p) level.

----

File:AracnhoB3H8FluxTS.out

2011-03-14T10:08:42Z

Pm08:

File:ArachnoB3H8GS.mol

2011-03-14T10:08:31Z

Pm08:

File:Borane flux IRC.gif

2011-03-14T08:34:36Z

Pm08:

Rep:Mod:pm08inorg4

2011-03-14T08:34:04Z

Pm08: New page: == Experiment 4 - Fluxional Process of the [B3H8]- Anion ==

== Experiment 4 - Fluxional Process of the [B3H8]- Anion ==

Rep:Mod:pm08expt5

2011-02-12T14:02:03Z

Pm08: /* Experiment 5: The Sharpless Catalytic Asymmetric Dihydroxylation of Styrene (Supporting Information) */

== Experiment 5: The Sharpless Catalytic Asymmetric Dihydroxylation of Styrene (Supporting Information) ==

<b>(DHQ)<sub>2</sub>PHAL ligand, uncomplexed</b>

<jmol>
<jmolApplet>
<title>DHQ2PHAL</title>
<color>white</color>
<size>650</size>
<uploadedFileContents>DHQ2PHAL.cml</uploadedFileContents>
</jmolApplet>
<jmolRadioGroup>
<item>
<script>spacefill 20%;</script>
<text>Ball and Stick</text>
</item>
<item>
<script>spacefill ON;</script>
<text>Space Filling</text>
</item>
</jmolRadioGroup>
</jmol>

<b>Osmate ester intermediate, complexed to ligand</b>

<jmol>
<jmolApplet>
<title>DHQ2PHAL</title>
<color>white</color>
<size>650</size>
<uploadedFileContents>DHQ2PHALOscomplex.cml</uploadedFileContents>
</jmolApplet>
<jmolRadioGroup>
<item>
<script>spacefill 20%;</script>
<text>Ball and Stick</text>
</item>
<item>
<script>spacefill ON;</script>
<text>Space Filling</text>
</item>
</jmolRadioGroup>
</jmol>

File:DHQ2PHAL.cml

2011-02-12T13:57:29Z

Pm08:

File:DHQ2PHALOscomplex.cml

2011-02-12T13:57:13Z

Pm08:

Rep:Mod:pm08expt5

2011-02-12T13:56:43Z

Pm08: New page: == Experiment 5: The Sharpless Catalytic Asymmetric Dihydroxylation of Styrene (Supporting Information) == <b>(DHQ)<sub>2</sub>PHAL ligand, uncomplexed</b> <jmol> <jmolApplet> <title>DHQ...

Rep:Mod:atbxz79364

2010-12-17T13:42:12Z

Pm08: /* The Pathway to Adamantane */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane<ref name='adamantane'>R.C.Fort, J.R.Schleyer, P.VR.Schleyer, ''Chem. Rev''. '''1964''', DOI: 10.1021/cr60229a004</ref>]]
In Module 1<ref name='Me!'>Philip Murray, Organic Compuational Lab, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:xxyte35130, 2010</ref>, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we rationalised as being due to a more favorable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall re-investigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, when looking through literature whilst studying that reaction, I found a paper<ref name='adamantane'>R.C.Fort, J.R.Schleyer, P.VR.Schleyer, ''Chem. Rev''. '''1964''', DOI: 10.1021/cr60229a004</ref>, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl<sub>3</sub>. AlCl<sub>3</sub> acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-structure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as "''(having) no direct precedent and is therefore subject to some suspicion. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.''"<ref name='adamantane'>R.C.Fort, J.R.Schleyer, P.VR.Schleyer, ''Chem. Rev''. '''1964''', DOI: 10.1021/cr60229a004</ref> This step will be examined, by modeling the reactant and product and looking for the transition state and reaction path, to determine its feasibility.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo- forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and carbon tetrahedral fragments, adjusting bond lengths, types and angles accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol<sup>-1</sup> more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Cyclopentadiene
</td>
<td>
-194.101058
</td>
<td>
-121800.3549
</td>
</tr>
<tr>
<td>
Endo-DCPD
</td>
<td>
-388.2280216
</td>
<td>
-243616.9658
</td>
</tr>
<tr>
<td>
Exo-DCPD
</td>
<td>
-388.2297763
</td>
<td>
-243618.0669
</td>
</tr>
</table>

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo- form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to to be the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, separated in space, in the correct relative orientations to each other, and the corresponding product diastereoisomer, with the atomic labeling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels Alder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. The vibrational modes of the transition states were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm<sup>-1</sup>, and in the exo-isomer, had magnitude 719cm<sup>-1</sup>. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Endo-DCPD TS
</td>
<td>
-388.1711242
</td>
<td>
-243581.2621
</td>
</tr>
<tr>
<td>
Exo-DCPD TS
</td>
<td>
-388.1667293
</td>
<td>
-243578.5043
</td>
</tr>
</table>

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new σ bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways together, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picture we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favorable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol<sup>-1</sup>, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better represented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised to DFT B3LYP 6-31G*. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

With the complex molecular geometry in the product and reactant, forming a guess transition state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transition state as having its charge again delocalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. To HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise initially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

The calculated activation energy on going from intermediate XX to TS is 26.44 kcalmol<sup>-1</sup>. The reaction from XX to XXI is very slightly endothermic with a reaction enthalpy of +0.77 kcalmol<sup>-1</sup>.

If this process possible? The authors proposed the pathway based upon analysis of the strain of the system - the highly strained endo-tetrahydrodicyclopentadiene rearranging to release strain. However, as we can see from the energies, there is no relief of strain, and the associated gain in stability, because the energy of the starting material and product are very similar, in fact the energy of the product as defined here is slightly higher in energy! This is because the two systems are both equally strained- by delocalising the charge, the systems are able to reduce some strain already, so the molecule is not confined to the bicyclic geometry, which the authors predicted above. So thermodynamically, there is no desire for this process to occur. But the energy difference is minimal between the two carbocations, so we would expect an equlibrium to exist between the two. The transition state energy is comparable to the Diels Alder reactions we previoously considered, so we expect it to be passable. Hence, we can say this process may be occuring, to set up an equlibrium between the two, but there is no great preference for either system. If the next reaction from XXI is fast, this could be removed from equlibrium and we would slowly see XX disappear, as XXI is converted. Hence, this step could be involved.

<table border='1'>
<tr>
<td colspan='3'>
'''Rearrangement Species Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Intermediate:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Intermediate XX
</td>
<td>
-389.7989889
</td>
<td>
-244602.7635
</td>
</tr>
<tr>
<td>
Transition State
</td>
<td>
-389.7568615
</td>
<td>
-244576.3281
</td>
</tr>
<tr>
<td>
Intermediate XXI
</td>
<td>
-389.8002186
</td>
<td>
-244603.5352
</td>
</tr>
</table>

----

<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79364

2010-12-17T13:41:22Z

Pm08: /* Following the reaction Path */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane]]
In Module 1<ref name='Me!'>Philip Murray, Organic Compuational Lab, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:xxyte35130, 2020</ref>, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we rationalised as being due to a more favorable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall re-investigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, when looking through literature whilst studying that reaction, I found a paper<ref name='adamantane'>R.C.Fort, J.R.Schleyer, P.VR.Schleyer, ''Chem. Rev''. '''1964''', DOI: 10.1021/cr60229a004</ref>, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl<sub>3</sub>. AlCl<sub>3</sub> acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-structure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as "''(having) no direct precedent and is therefore subject to some suspicion. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.''"<ref name='adamantane'>R.C.Fort, J.R.Schleyer, P.VR.Schleyer, ''Chem. Rev''. '''1964''', DOI: 10.1021/cr60229a004</ref> This step will be examined, by modeling the reactant and product and looking for the transition state and reaction path, to determine its feasibility.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo- forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and carbon tetrahedral fragments, adjusting bond lengths, types and angles accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol<sup>-1</sup> more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Cyclopentadiene
</td>
<td>
-194.101058
</td>
<td>
-121800.3549
</td>
</tr>
<tr>
<td>
Endo-DCPD
</td>
<td>
-388.2280216
</td>
<td>
-243616.9658
</td>
</tr>
<tr>
<td>
Exo-DCPD
</td>
<td>
-388.2297763
</td>
<td>
-243618.0669
</td>
</tr>
</table>

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo- form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to to be the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, separated in space, in the correct relative orientations to each other, and the corresponding product diastereoisomer, with the atomic labeling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels Alder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. The vibrational modes of the transition states were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm<sup>-1</sup>, and in the exo-isomer, had magnitude 719cm<sup>-1</sup>. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Endo-DCPD TS
</td>
<td>
-388.1711242
</td>
<td>
-243581.2621
</td>
</tr>
<tr>
<td>
Exo-DCPD TS
</td>
<td>
-388.1667293
</td>
<td>
-243578.5043
</td>
</tr>
</table>

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new σ bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways together, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picture we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favorable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol<sup>-1</sup>, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better represented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised to DFT B3LYP 6-31G*. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

With the complex molecular geometry in the product and reactant, forming a guess transition state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transition state as having its charge again delocalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. To HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise initially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

The calculated activation energy on going from intermediate XX to TS is 26.44 kcalmol<sup>-1</sup>. The reaction from XX to XXI is very slightly endothermic with a reaction enthalpy of +0.77 kcalmol<sup>-1</sup>.

If this process possible? The authors proposed the pathway based upon analysis of the strain of the system - the highly strained endo-tetrahydrodicyclopentadiene rearranging to release strain. However, as we can see from the energies, there is no relief of strain, and the associated gain in stability, because the energy of the starting material and product are very similar, in fact the energy of the product as defined here is slightly higher in energy! This is because the two systems are both equally strained- by delocalising the charge, the systems are able to reduce some strain already, so the molecule is not confined to the bicyclic geometry, which the authors predicted above. So thermodynamically, there is no desire for this process to occur. But the energy difference is minimal between the two carbocations, so we would expect an equlibrium to exist between the two. The transition state energy is comparable to the Diels Alder reactions we previoously considered, so we expect it to be passable. Hence, we can say this process may be occuring, to set up an equlibrium between the two, but there is no great preference for either system. If the next reaction from XXI is fast, this could be removed from equlibrium and we would slowly see XX disappear, as XXI is converted. Hence, this step could be involved.

<table border='1'>
<tr>
<td colspan='3'>
'''Rearrangement Species Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Intermediate:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Intermediate XX
</td>
<td>
-389.7989889
</td>
<td>
-244602.7635
</td>
</tr>
<tr>
<td>
Transition State
</td>
<td>
-389.7568615
</td>
<td>
-244576.3281
</td>
</tr>
<tr>
<td>
Intermediate XXI
</td>
<td>
-389.8002186
</td>
<td>
-244603.5352
</td>
</tr>
</table>

----

<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79364

2010-12-17T13:39:19Z

Pm08: /* The Pathway to Adamantane */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane]]
In Module 1<ref name='Me!'>Philip Murray, Organic Compuational Lab, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:xxyte35130, 2020</ref>, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we rationalised as being due to a more favorable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall re-investigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, when looking through literature whilst studying that reaction, I found a paper<ref name='adamantane'>R.C.Fort, J.R.Schleyer, P.VR.Schleyer, ''Chem. Rev''. '''1964''', DOI: 10.1021/cr60229a004</ref>, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl<sub>3</sub>. AlCl<sub>3</sub> acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-structure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as "''(having) no direct precedent and is therefore subject to some suspicion. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.''"<ref name='adamantane'>R.C.Fort, J.R.Schleyer, P.VR.Schleyer, ''Chem. Rev''. '''1964''', DOI: 10.1021/cr60229a004</ref> This step will be examined, by modeling the reactant and product and looking for the transition state and reaction path, to determine its feasibility.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo- forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and carbon tetrahedral fragments, adjusting bond lengths, types and angles accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol<sup>-1</sup> more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Cyclopentadiene
</td>
<td>
-194.101058
</td>
<td>
-121800.3549
</td>
</tr>
<tr>
<td>
Endo-DCPD
</td>
<td>
-388.2280216
</td>
<td>
-243616.9658
</td>
</tr>
<tr>
<td>
Exo-DCPD
</td>
<td>
-388.2297763
</td>
<td>
-243618.0669
</td>
</tr>
</table>

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo- form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to to be the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, separated in space, in the correct relative orientations to each other, and the corresponding product diastereoisomer, with the atomic labeling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels Alder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. The vibrational modes of the transition states were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm<sup>-1</sup>, and in the exo-isomer, had magnitude 719cm<sup>-1</sup>. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Endo-DCPD TS
</td>
<td>
-388.1711242
</td>
<td>
-243581.2621
</td>
</tr>
<tr>
<td>
Exo-DCPD TS
</td>
<td>
-388.1667293
</td>
<td>
-243578.5043
</td>
</tr>
</table>

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new σ bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways together, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picture we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favorable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol<sup>-1</sup>, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better represented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised to DFT B3LYP 6-31G*. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

With the complex molecular geometry in the product and reactant, forming a guess transition state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transition state as having its charge again delocalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. To HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise initially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

The calculated activation energy on going from intermediate XX to TS is 26.44 kcalmol<sup>-1</sup>. The reaction from XX to XXI is very slightly endothermic with a reaction enthalpy of +0.77 kcalmol<sup>-1</sup>.

If this process possible? The authors proposed the pathway based upon analysis of the strain of the system - the highly strained endo-tetrahydrodicyclopentadiene rearranging to release strain. However, as we can see from the energies, there is no relief of strain, and the associated gain in stability, because the energy of the starting material and product are very similar, in fact the energy of the product as defined here is slightly higher in energy! This is because the two systems are both equally strained- by delocalising the charge, the systems are able to reduce some strain already, so the molecule is not confined to the bicyclic geometry, which the authors predicted above. So thermodynamically, there is no desire for this process to occur. But the energy difference is minimal between the two carbocations, so we would expect an equlibrium to exist between the two. The transition state energy is comparable to the Diels Alder reactions we previoously considered, so we expect it to be passable. Hence, we can say this process may be occuring, to set up an equlibrium between the two, but there is no great preference for either system. If the next reaction from XXI is fast, this could be removed from equlibrium and we would slowly see XX disappear, as XXI is converted. Hence, this step could be involved.

<table border='1'>
<tr>
<td colspan='3'>
'''Rearrangement Species Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Intermediate:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Intermediate XX
</td>
<td>
-389.7989889
</td>
<td>
-244602.7635
</td>
</tr>
<tr>
<td>
Transition State
</td>
<td>
-389.7568615
</td>
<td>
-244576.3281
</td>
</tr>
<tr>
<td>
Intermediate XXI
</td>
<td>
-389.8002186
</td>
<td>
-244603.5352
</td>
</tr>
</table>

----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:28:51Z

Pm08: /* Following the reaction pathway */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two π systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theory. When we changed to B3LYP theory, the energy of this mode was 525cm<sup>-1</sup>. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5-hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==
<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref>
<ref name='pericyclic2'>T.L.Gilchrist, R.C.Storr, ''Organic Reactions and Orbital Symmetry'', 1972</ref>
Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the π orbital, which in many alkenes is normally our HOMO, being moved to HOMO-2, because of the stabilising nature of the resonance with the ester. The HOMO is mostly of carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find that the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene π orbitals, which is antisymmetric with respect to the plane, and the LUMO is π* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal electron demand.<ref name='Spivey'>A.C.Spivey, ''Heteroaromatic chemistry'' Lecture Course, 2010</ref> Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the π/π* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orientations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of the product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

<table border='1'>
<tr>
<td>
'''Exo-TS'''
</td>
<td>
'''Endo-TS'''
</td>
</tr>
<tr>
<td>
[[Image:pm08MADAExoTSHOMO.png|150px]]
</td>
<td>
[[Image:pm08MADAEndoTSHOMO.png|150px]]
</td>
</tr>
</table>

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply π* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl π* in character, as well as the alkene π*. In the endo-transition state, this π system sits over the newly forming alkene, and they can form a symmetry allowed combination. Because this is a HOMO/LUMO interaction, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this π system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy changes discussed.

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH<sub>2</sub>CH<sub>2</sub> unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is in fact a transition state we have found, by accident, with one imaginary mode of magnitude 154cm<sup>-1</sup>! Animating the vibration, we find that it is the puckering of the CH<sub>2</sub>CH<sub>2</sub> group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered minimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclic fragment, and carbon tetrahedral fragments, then adjusting the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol<sup>-1</sup> lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH<sub>2</sub>CH<sub>2</sub> H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start point, to allow the interpolation between this structure and the corresponding product isomer to give the transition state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol<sup>-1</sup> higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favorable, stabilising secondary orbital overlap between the maleic anhydride carbonyl π system, and the forming double bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electronic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Because the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reactants and products to DFT B3LYP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol<sup>-1</sup>. That for the exo pathway is calculated at 18.30 kcalmol<sup>-1</sup>. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol<sup>-1</sup>. That for the exo-pathwas is at -29.69 kcalmol<sup>-1</sup>. Hence, the endo pathway is also favoured under theromdynamic conditions.

We should note that all the energies reported here are from calculations on the free, isolated molecules. Diels Alder reactions can be influenced by the solvent, though usually less than ionic species. Hence, we could include a solvation model in our calculation, to correct for this.

</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:27:01Z

Pm08: /* Following the reaction pathway */

Rep:Mod:atbxz79363

2010-12-17T13:24:11Z

Pm08: /* Optimising Transition States */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two π systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theory. When we changed to B3LYP theory, the energy of this mode was 525cm<sup>-1</sup>. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5-hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==
<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref>
<ref name='pericyclic2'>T.L.Gilchrist, R.C.Storr, ''Organic Reactions and Orbital Symmetry'', 1972</ref>
Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the π orbital, which in many alkenes is normally our HOMO, being moved to HOMO-2, because of the stabilising nature of the resonance with the ester. The HOMO is mostly of carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find that the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene π orbitals, which is antisymmetric with respect to the plane, and the LUMO is π* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal electron demand.<ref name='Spivey'>A.C.Spivey, ''Heteroaromatic chemistry'' Lecture Course, 2010</ref> Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the π/π* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orientations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of the product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

<table border='1'>
<tr>
<td>
'''Exo-TS'''
</td>
<td>
'''Endo-TS'''
</td>
</tr>
<tr>
<td>
[[Image:pm08MADAExoTSHOMO.png|150px]]
</td>
<td>
[[Image:pm08MADAEndoTSHOMO.png|150px]]
</td>
</tr>
</table>

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply π* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl π* in character, as well as the alkene π*. In the endo-transition state, this π system sits over the newly forming alkene, and they can form a symmetry allowed combination. Because this is a HOMO/LUMO interaction, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this π system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy changes discussed.

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH<sub>2</sub>CH<sub>2</sub> unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is in fact a transition state we have found, by accident, with one imaginary mode of magnitude 154cm<sup>-1</sup>! Animating the vibration, we find that it is the puckering of the CH<sub>2</sub>CH<sub>2</sub> group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered minimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclic fragment, and carbon tetrahedral fragments, then adjusting the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol<sup>-1</sup> lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH<sub>2</sub>CH<sub>2</sub> H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start point, to allow the interpolation between this structure and the corresponding product isomer to give the transition state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol<sup>-1</sup> higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favorable, stabilising secondary orbital overlap between the maleic anhydride carbonyl π system, and the forming double bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:22:49Z

Pm08: /* Optimising Reactants and Products */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two π systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theory. When we changed to B3LYP theory, the energy of this mode was 525cm<sup>-1</sup>. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5-hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==
<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref>
<ref name='pericyclic2'>T.L.Gilchrist, R.C.Storr, ''Organic Reactions and Orbital Symmetry'', 1972</ref>
Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the π orbital, which in many alkenes is normally our HOMO, being moved to HOMO-2, because of the stabilising nature of the resonance with the ester. The HOMO is mostly of carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find that the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene π orbitals, which is antisymmetric with respect to the plane, and the LUMO is π* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal electron demand.<ref name='Spivey'>A.C.Spivey, ''Heteroaromatic chemistry'' Lecture Course, 2010</ref> Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the π/π* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orientations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of the product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

<table border='1'>
<tr>
<td>
'''Exo-TS'''
</td>
<td>
'''Endo-TS'''
</td>
</tr>
<tr>
<td>
[[Image:pm08MADAExoTSHOMO.png|150px]]
</td>
<td>
[[Image:pm08MADAEndoTSHOMO.png|150px]]
</td>
</tr>
</table>

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply π* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl π* in character, as well as the alkene π*. In the endo-transition state, this π system sits over the newly forming alkene, and they can form a symmetry allowed combination. Because this is a HOMO/LUMO interaction, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this π system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy changes discussed.

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH<sub>2</sub>CH<sub>2</sub> unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is in fact a transition state we have found, by accident, with one imaginary mode of magnitude 154cm<sup>-1</sup>! Animating the vibration, we find that it is the puckering of the CH<sub>2</sub>CH<sub>2</sub> group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered minimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclic fragment, and carbon tetrahedral fragments, then adjusting the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol<sup>-1</sup> lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH<sub>2</sub>CH<sub>2</sub> H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:19:58Z

Pm08: /* Orbital Symmetry */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two π systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theory. When we changed to B3LYP theory, the energy of this mode was 525cm<sup>-1</sup>. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5-hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==
<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref>
<ref name='pericyclic2'>T.L.Gilchrist, R.C.Storr, ''Organic Reactions and Orbital Symmetry'', 1972</ref>
Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the π orbital, which in many alkenes is normally our HOMO, being moved to HOMO-2, because of the stabilising nature of the resonance with the ester. The HOMO is mostly of carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find that the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene π orbitals, which is antisymmetric with respect to the plane, and the LUMO is π* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal electron demand.<ref name='Spivey'>A.C.Spivey, ''Heteroaromatic chemistry'' Lecture Course, 2010</ref> Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the π/π* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orientations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of the product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

<table border='1'>
<tr>
<td>
'''Exo-TS'''
</td>
<td>
'''Endo-TS'''
</td>
</tr>
<tr>
<td>
[[Image:pm08MADAExoTSHOMO.png|150px]]
</td>
<td>
[[Image:pm08MADAEndoTSHOMO.png|150px]]
</td>
</tr>
</table>

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply π* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl π* in character, as well as the alkene π*. In the endo-transition state, this π system sits over the newly forming alkene, and they can form a symmetry allowed combination. Because this is a HOMO/LUMO interaction, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this π system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:18:14Z

Pm08: /* Orbital Symmetry */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two π systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theory. When we changed to B3LYP theory, the energy of this mode was 525cm<sup>-1</sup>. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5-hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==
<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref>
Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the π orbital, which in many alkenes is normally our HOMO, being moved to HOMO-2, because of the stabilising nature of the resonance with the ester. The HOMO is mostly of carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find that the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene π orbitals, which is antisymmetric with respect to the plane, and the LUMO is π* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal electron demand.<ref name='Spivey'>A.C.Spivey, ''Heteroaromatic chemistry'' Lecture Course, 2010</ref> Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the π/π* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orientations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of the product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

<table border='1'>
<tr>
<td>
'''Exo-TS'''
</td>
<td>
'''Endo-TS'''
</td>
</tr>
<tr>
<td>
[[Image:pm08MADAExoTSHOMO.png|150px]]
</td>
<td>
[[Image:pm08MADAEndoTSHOMO.png|150px]]
</td>
</tr>
</table>

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply π* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl π* in character, as well as the alkene π*. In the endo-transition state, this π system sits over the newly forming alkene, and they can form a symmetry allowed combination. Because this is a HOMO/LUMO interaction, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this π system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:11:51Z

Pm08: /* Following the reaction pathway */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two π systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theory. When we changed to B3LYP theory, the energy of this mode was 525cm<sup>-1</sup>. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5-hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:11:23Z

Pm08: /* Optimising the Transition State */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two π systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theory. When we changed to B3LYP theory, the energy of this mode was 525cm<sup>-1</sup>. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:11:02Z

Pm08: /* Optimising the Transition State */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two π systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theory. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:10:31Z

Pm08: /* Reactants */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two π systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:09:45Z

Pm08: /* Orbital Symmetry in the Diels Alder Reaction */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations.<ref name='pericyclic'>http://www.ch.ic.ac.uk/local/organic/pericyclic/</ref> Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two pi systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T13:08:33Z

Pm08: /* The Diels Alder Cycloaddition between Butadiene and Ethene */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry properties of the Frontier orbitals of the reactants, we will show that this reaction is allowed, and make a prediction as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transition state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloadditon between Maleic anhydride acting as the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations. Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Because of the symmetry constraint, the geometry of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from π bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

A typical value for an sp<sup>3</sup>C-sp<sup>3</sup>C bond is 1.54Å. Likewise, that for sp<sup>2</sup>C-sp<sup>2</sup>C is 1.32Å. IF we measure the lengths of bonds in the transition state, we find that the σ bond of the butadiene is now 1.41Å, and the π bonds of the butadiene are 1.38Å. These are in between the typical values, showing that the bonds are changing their character, as the orbitals mix. Likewise, the ethene bond distance is increased to 1.39Å in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinations.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minima and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5<sup>o</sup> intervals, i.e a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomalous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two pi systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stronger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclic system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST2 calculation interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labeling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis-conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the π system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to re-optimise our HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol<sup>-1</sup>. The calculated enthalpy change of reaction is -43.1 kcalmol<sup>-1</sup>.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T12:56:15Z

Pm08: /* Following the reaction pathway */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry propoerties of the Frontier orbitals of the reactants, we will show that this reactio is allowed, and make a prediciton as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transiiton state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloaditon between Maleic anhydride acting ad the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations. Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Becuase of the symmetry constraint, the geomerty of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from pi bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinsaions.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minim and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5o intervals, ie a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomolous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two pi systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stornger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclo system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels ALder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST 2 calcualtion interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labelling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the pi system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to reoptimiseour HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol-1. The calculated free eneergy change of reaction is -43.1 kcalmol-1.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>

----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79362

2010-12-17T12:53:40Z

Pm08:

=The Cope Rearrangement=
<div align='justify'>
[[Image:pm08copescheme.png|frame|The Cope Rearrangement, a [3,3]-Sigmatropic alkyl shift]]
The Cope Rearrangement involves a concerted [3,3]-Sigmatropic alkyl shift in a 1,5-diene system. The reaction proceeds thermally, via a Huckel topography, with Suprafacial sterochemistry. We are going to show this statement to be true, by using computational methods to study this reaction.

In the most simple case of a Cope reaction, 1,5-hexadiene rearranges. The product is the same as the reactant, but with the order of the atoms changed. We shall initially investigate this reaction, first looking at the geometry of 1,5-hexadiene to determine the most stable conformer, and why, and then explore various methods of optimising the transition state of the reaction.

==The Cope Rearrangement of 1,5-Hexadiene==
===Optimising the Geometry of 1,5-Hexadiene===

[[Image:pm0815hexadiene.png|left]]
Initially, we shall optimise a molecule of 1,5-Hexadiene, exploring the geometries of different conformations, asking why certain conformations are lower in energy than others.

Using the Gaussview 3.09 GUI, a molecule of 1,5-hexadiene was created, with anti-stereochemistry across the central C-C bond (the Dihedral angle was set to 180<sup>o</sup>). This was optimised using the HF/3-21G Level of theory. The calculation optimised the molecule to a C<sub>2</sub>-symmetric geometry, with energy -231.69260 Eh = -145389.42 kcalmol<sup>-1</sup>. This corresponds to the Anti-1 geometry listed in appendix 1.<ref name='one'>[[Mod:phys3#Appendix_1]]</ref> According to appendix 1, we have found the lowest energy conformation of anti-1,5-hexadiene.

Next, a molecule of gauche-1,5-hexadiene was created (the Dihedral angle across the central C-C set to 60<sup>o</sup>). An optimisation was again run, using the same level of theory. The optimised geometry was again C<sub>2</sub>-symmetric, with an energy of -231.69167 Eh = -145388.84 kcal mol<sup>-1</sup>. The energy of this gauche conformation, corresponding to Gauche-2 in appendix 1<ref name='one'>[[Mod:phys3#Appendix_1]]</ref>, was 0.59Kcalmol<sup>-1</sup> higher in energy than the Anti-1 conformation we first optimised to. Why was this conformation higher in energy than the anti conformation?<ref name='rzepa'>http://www.ch.ic.ac.uk/local/organic/conf/</ref>

[[Image:pm08antigauchesigmaenergy.png|left]]
We need to consider the favorable secondary orbital overlap between σ/σ* orbitals in anti-relationships. Both conformations are staggered, so every bond has an anti-relationship to another bond. In the anti-conformer, if we look at those relationships, we see we have 2σ<sub>CC</sub>/σ<sub>CC</sub>* and 4σ<sub>CH</sub>/σ<sub>CH</sub>*. In the gauche-conformer, we now have 2σ<sub>CC</sub>/σ<sub>CH</sub>*, 2σ<sub>CH</sub>/σ<sub>CC</sub>* and 2σ<sub>CH</sub>/σ<sub>CH</sub>*. We can draw up a qualitative energy level diagram showing E<sub>2</sub> stabilising secondary interaction between orbitals, to explain the preference for the anti-conformation.

First, we define the position of the CC and CH σ and σ* orbitals. We know that the σ<sub>CC</sub> is lower in energy than the σ<sub>CH</sub>, because the two C sp<sup>3</sup> orbitals are equal in energy, so are split more than a CH pair, because the C sp<sup>3</sup> and H s orbital are apart in energy. The same is true for the σ* orbitals. In the anti conformation, the secondary overlap between σ<sub>CC</sub>/σ<sub>CC</sub>* produces a stabilisation. Likewise for the σ<sub>CH</sub>/σ<sub>CH</sub>* overlap. We would expect the σ<sub>CC</sub>/σ<sub>CC</sub>* overlap to be slightly more stabilising than the σ<sub>CH</sub>/σ<sub>CH</sub>* stabilisation, because the σ/σ* gap would be less, because the C FO's atoms are more evenly matched in energy. In the gauche-conformer, we also have the σ<sub>CH</sub>/σ<sub>CH</sub>* overlap, but now no σ<sub>CC</sub>/σ<sub>CC</sub>* overlap. Instead we have σ<sub>CC</sub>/σ<sub>CH</sub>* overlap, which is very little stabilising, because the orbitals are far apart in energy, and a σ<sub>CH</sub>/σ<sub>CC</sub>* overlap, which is more stabilising than the σ<sup>CH</sup>/σ<sub>CH</sub>* overlap, because the orbitals are closer in energy. Adding up the total number of interactions, we would expect the anti-conformer to be lower in energy, because, overall, the overlap of HOMO σ/σ* pairs will be more stabilising that the overlap of HOMO and HETRO σ/σ* pairs. This agrees with the resulting energy from calculation.

However, we also need to consider interactions between non-bonded pairs of atoms - The van der Waals interaction. This is the anisotropic interaction between two non-bonded atoms separated by a distance r. If r is very small, then the interaction is repulsive, due to n/n and e/e repulsions. If r is large, then the atoms are too far to be influenced. If r however is ideal, then the stabilising n/e Coulombic interaction is balanced by n/n and e/e and overall we have a lower energy. This is the sum of the two van der Waals radii of the atoms involved. Even if the distance is slightly larger than this distance though, the interaction is still attractive, since this is over a large range. If we inspect the anti and gauche conformers, we see that the Gauche conformer sets up more of these interactions by folding in on itself. However, as we have seen, overall, the energy of the anti conformer is lower, but not by a great deal.

Based on what we have just said, we could imagine a lower energy gauche-conformer. If in the current gauche conformer, one CH<sub>2</sub>CH group twisted 180<sup>o</sup>, then one H atoms is moved within the molecule somewhat, and into the attractive region of more carbon and hydrogen atoms. Also, this twist means the two 'halves' of the molecule are not not directly over each other in space - before, they were, but they were far away, so steric bumping is unlikely, but may make a slight repulsive contribution. This has however now been removed. We took the gauche-conformation, twisted a CH<sub>2</sub>CH group by 180<sup>o</sup>, and then optimised to HF/3-21G level of theory, and the resulting energy was -231.69266 Eh = -145389.46 kcalmol<sup>-1</sup>. The resulting geometry was C<sub>1</sub>-symmetric, corresponding to Gauche-3 in Appendix 1<ref name='one'>[[Mod:phys3#Appendix_1]]</ref>. This is 0.62 kcalmol<sup>-1</sup> more stable than the other Gauche conformer, by virtue of extra attractive van der Waals interactions. Also, this is 0.036 kcalmol<sup>-1</sup> more stable than the anti conformer. This is surprising, showing that the van der Waals interactions do make a significant contribution to the energy of the molecule, and in this case, overall, the energy is lower, by a small amount. However, in the Gauche conformers, we saw we have many van der Waals interactions, whereas in the anti conformer, we had few, so we can say overall, that on the anti-conformer, the σ/σ* is greater than in the gauche-conformers.

We should also be able to imagine another low-energy conformation of the anti-geometry. In Anti-1, the CH<sub>2</sub>CH groups are both twisted the same way with respect to the central anti-linkage, resulting in C<sub>2</sub> symmetry. Above, we twisted one group and found a lower energy gauche conformer. Let's do the same now. Twisting one CH<sub>2</sub>CH group and optimising to HF/3-21G resulted in a C<sub>i</sub>-symmetric geometry with energy -231.692535 Eh = -145389.38 kcalmol<sup>-1</sup>, corresponding to Anti-2 in appendix 1<ref name='one'>[[Mod:phys3#Appendix_1]]</ref>. This is 0.042 kcalmol<sup>-1</sup> higher in energy than the Anti-1 conformer. In this case, twisting of the group did not result in a lower energy conformer.

<table border='1'>
<tr>
<td colspan='5'>
'''1,5-Hexadiene Conformers /HF 3-21G'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Anti-1'''
</td>
<td>
'''Anti-2'''
</td>
<td>
'''Gauche-2'''
</td>
<td>
'''Gauche-3'''
</td>
</tr>
<tr>
<td valign='top'>
'''Geometry'''
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Anti-1</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copeanti1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Anti-2</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copeanti2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Gauche-2</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copegauche2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Gauche-3</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copegauche3.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td>
'''Energy /Eh'''
</td>
<td>
-231.69260
</td>
<td>
-231.69254
</td>
<td>
-231.69167
</td>
<td>
-231.69266
</td>
</tr>
<tr>
<td>
'''Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
0.036
</td>
<td>
0.078
</td>
<td>
0.62
</td>
<td>
0.0
</td>
</tr>
</table>

Let us make a comparison between different levels of theory. Above, we used HF/3-21G. Now, we are going to take our low-energy conformer, listed in the table above and re-optimise, using DFT/B3LYP/6-31G*. We shall also carry out a frequency analysis for these geometries, to verify that we have indeed reached a minimum.

<table border='1'>
<tr>
<td colspan='7'>
'''Comparison between levels of theory in the optimisation of 1,5-Hexadiene'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''HF 3-21G Energy /Eh'''
</td>
<td>
'''DFT B3LYP 6-31G* Energy /Eh'''
</td>
<td>
'''Difference /Eh'''
</td>
<td>
'''HF 3-21G Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
'''DFT B3LYP 6-31G* Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
'''Imaginary modes /cm<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''Anti-1 (C<sub>2</sub>)'''
</td>
<td>
-231.69260
</td>
<td>
-234.61180
</td>
<td>
2.91920
</td>
<td>
0.036
</td>
<td>
0.0
</td>
<td>
-8.41

-3.82
</td>
</tr>
<tr>
<td>
'''Anti-2 (C<sub>i</sub>)'''
</td>
<td>
-231.69254
</td>
<td>
-234.61172
</td>
<td>
2.91902
</td>
<td>
0.078
</td>
<td>
0.052
</td>
<td>
-6.20
</td>
</tr>
<tr>
<td>
'''Gauche-2 (C<sub>2</sub>)'''
</td>
<td>
-231.69167
</td>
<td>
-234.61069
</td>
<td>
2.91867
</td>
<td>
0.62
</td>
<td>
0.70
</td>
<td>
-13.97

-13.36

-11.10
</td>
</tr>
<tr>
<td>
'''Gauche-3 (C<sub>1</sub>)'''
</td>
<td>
-231.69266
</td>
<td>
-234.61133
</td>
<td>
2.91918
</td>
<td>
0.0
</td>
<td>
0.30
</td>
<td>
-4.40
</td>
</tr>
</table>

Between the two sets of theory, we see that the higher level DFT method has calculated a different relative energy order of our conformers. The two levels of theory do however give the same order of stabilities between the pairs of anti- and gauche- conformers, so this suggests that the DFT calculated a greater σ/σ* stabilising interaction, or a weak vdW stabilising interaction. Hence, the gauche are calculated to be less stable than the anti conformers under DFT/B3LYP/6-31G*.

There is however, a slightly worrying result when we look at the imaginary frequencies. These should all be zero, if we have indeed optimised to a minimum. I think perhaps using this mid level basis set, that the geometry hasn't quite reached the minimum. Because the energy differences are very small between conformers, a slight difference in geometry could lead us to an incorrect order of relative energies. Hence, the optimisation was rerun again, from the DFT result, this time specifying very tight convergence criteria, and int=ultrafine This is computationally expensive, but I think it is necessary to establish which is the lowest energy conformer. The results:

<table border='1'>
<tr>
<td colspan='4'>
'''DFT B3LYP 6-31G* Very tight optimisation 1,5-Hexadiene Conformers'''
</td>
</tr>
<tr>
<td>
'''Energy /Eh'''
</td>
<td>
'''Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
'''Imaginary modes /cm<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''Anti-1 (C<sub>2</sub>)'''
</td>
<td>
-234.61179
</td>
<td>
0.0
</td>
<td>
-6.6

-3.2
</td>
</tr>
<tr>
<td>
'''Anti-2 (C<sub>i</sub>)'''
</td>
<td>
-234.61171
</td>
<td>
0.051
</td>
<td>
-5.6

-1.9
</td>
</tr>
<tr>
<td>
'''Gauche-2 (C<sub>2</sub>)'''
</td>
<td>
-234.61070
</td>
<td>
0.68
</td>
<td>
-5.8

-5.4

-4.2
</td>
</tr>
<tr>
<td>
'''Gauche-3 (C<sub>1</sub>)'''
</td>
<td>
-234.61133
</td>
<td>
0.29
</td>
<td>
-0.0004
</td>
</tr>
</table>

This very tight convergence reduced the magnitude of all of the imaginary modes, showing the geometry is moving toward the bottom of the potential well. The key result here is that the energy changed only by ~0.01 kcalmol<sup>-1</sup>, and the order of conformers did not change. If we consider the potential surface for this molecule, we expect wells for the conformers we have found. For the two pairs of anti and gauche conformers, the geometry difference is not a great deal, so the wells are close, and probably not very steep barrier between them. Hence, this may also explain why we get small imaginary frequencies – we are not at a transition structure, but in a shallow well, not quite at the bottom. Because this result agrees with that for the quicker calculation, we shall use the DFT B3LYP 6-31G* theory for further analysis.

[[Image:pm08anti2thermochemistry.png|right]]
The energies reported are for the conformations at 0K. Carrying out a frequency analysis allows us to make a correction to other temperatures, specified using a readisotopes keyword. Using the Anti-2 conformer, we are going to investigate the effect of increasing temperature on the energy of the system, taking into account the thermal correction, by calculating the thermal correction at a range of temperatures, by specifying a frequency calculation to the DFT B3LYP 6-31G* level, with the readisotopes tag, on a DFT B3LYP 6-31Gd optimised geometry, and then plotting the resulting Sum of Electronic, ZPE and thermal energies.

We initially see that at low temperatures, the energy is increasing, at an increasing rate with increasing temperature, until a point where the increase in energy of the system is linear with temperature. At T=0K, all the molecules are in their vibrational ground state. As T is raised, but kept low, the first few vibrationally excited states begin to be populated. Increasing the thermal energy further will populate more states until it gets to a point where all the vibrational states are filled. In this regime, we see an increasing rate of change of energy with temperature. At this point, the discrete properties of the molecules can be treated classically, i.e the vibrational temperature. After this temperature is surpassed, the molecule behaves classically, and its increase in energy is linear with temperature.

===Locating the Transition State Structures===

[[Image:pm08copechairboatts.png|left]]
We are going to use a variety of methods to explore the transition state geometries of this rearrangement. Initially, we shall form a guess, consisting of two allyl- fragments separated in space, with the correct symmetry to hopefully optimise to the transition structure. We shall use the Berny TS method to optimise, and also the 'Frozen' Coordinate, two-stage optimisation method. Then, we shall use the QST2 method, now, not forming a transition state guess, but interpolating between the starting material and product.

If we consider two allyl fragments separated in space, we can form two potential transition state structures, corresponding to chair and boat cyclohexyl-like geometries. We shall explore both reaction pathways, via chair and boat TS structures, to determine which is the lower energy, and hence more favorable process.

====Berny Optimisation====
[[Image:pm08copetsguesses.png|right]]
Using Gaussview 3.09 GUI, an allyl, C<sub>3</sub>H<sub>5</sub>, fragment was created. This was optimised using HF 3-21G theory, and the resulting geometry was then used to build our transition state guesses. Two of these fragments were placed face on, one overlapping directly, to give a C<sub>2</sub>v-symmetric geometry - Boat, and once with one fragment rotated, with a terminal C overlapping with terminal H on the other fragment, to give a C<sub>2</sub>h-symmetric geometry - Chair. The two allyl fragments were set 2.2Å apart in both starting guesses.

These structures were then optimised to a Transition State, using the Berny method and HF/3-21G theory, calculating the force constants once. The resulting geometries are shown below. In both structures, the central C atom of the allyl fragments pucker away from the other fragment slightly. In the chair C<sub>2</sub>h structure, the terminal C atoms are separated by 2.02Å. In the C<sub>2</sub>v boat, they are separated by 2.14Å.

<table border='1'>
<tr>
<td colspan='2'>
'''HF 3-21G TS(Berny) Opt results'''
</td>
</tr>
<tr>
<td>
Chair-C<sub>2</sub>h
</td>
<td>
Boat-C<sub>2</sub>v
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Cope Chair TS Benry Optimisation result</title><color>white</color><size>150</size>
<script>rotate; measure 1 10;</script>
<uploadedFileContents>pm08copechairtsberny.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Cope Boat TS Benry Optimisation result</title><color>white</color><size>150</size>
<script>rotate; measure 1 10;</script>
<uploadedFileContents>pm08copeboattsberny.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Note that although Jmol draws these as propene fragments, the two C-C bond lengths in each fragment are equal and they are in reality allyl- like. How do we know these are transition states? We look for one imaginary mode, corresponding to the displacement either side of the transition state. In the Chair-C<sub>2</sub>h TS, we find exactly that, an imaginary frequency with magnitude 817cm<sup>-1</sup>. Likewise, in the Boat-C<sub>2</sub>v TS, at magnitude 840cm<sup>-1</sup>. Animating these imaginary modes, we see each allyl fragment bend back and forth from each other. This is the Cope rearrangement.

<table border='1'>
<tr>
<td colspan='2'>
'''HF 3-21G TS(Berny) Opt Imaginary modes'''
</td>
</tr>
<tr>
<td>
'''Chair-C<sub>2</sub>h'''
</td>
<td>
'''Boat-C<sub>2</sub>v'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Cope Chair TS Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 3;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834132.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Cope Boat TS Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 3;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834131.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td>
-817cm<sup>-1</sup>
</td>
<td>
-840cm<sup>-1</sup>
</td>
</tr>
</table>

====Frozen Coordinate Optimisation====

The transition state structure guesses were taken and using the redundant coordinate tool in Gaussview, the terminal C atoms of the two fragments were frozen, at a set distance of 2.2Å apart. What this does is fix the position of these atoms when we optimise the structure. We carried out a HF/3-21G Opt=Modredundant calculation. In the resulting geometry, the central C atoms had puckered out slightly, as they did above, but as we said, the terminal atoms stayed fixed. Then we took this resulting geometry and optimised again, using the same theory, this time without the condition of being fixed, but to differentiate along the forming and breaking bonds to find the transition state. The value in this method is that we do not have to calculate force constants, which for large jobs will be less computationally expensive.

How do these compare to the Berny Results? If we measure the following geometric parameters, in both the chair and boat structures for both optimisation methods, we find them to be be identical to 0.01Å and 0.1<sup>o</sup>. Hence, we can say that for this simple system, both methods of optimising a transition state from a guess are equally valid.

<table border='1'>
<tr>
<td colspan='5'>
'''Comparing Optimised TS structures for two different methods'''
</td>
</tr>
<tr>
<td colspan='5'>
[[Image:pm08guesstscompare.png]]
</td>
</tr>
<tr>
<td rowspan='2'>
'''Parameter'''
</td>
<td colspan='2'>
'''HF 3-21G Berny TS Optimisation'''
</td>
<td colspan='2'>
'''HF 3-21G Frozen Coordinate TS Optimisation'''
</td>
</tr>
<tr>
<td>
Chair
</td>
<td>
Boat
</td>
<td>
Chair
</td>
<td>
Boat
</td>
</tr>
<tr>
<td>
a
</td>
<td>
2.02
</td>
<td>
2.14
</td>
<td>
2.02
</td>
<td>
2.14
</td>
</tr>
<tr>
<td>
b
</td>
<td>
2.88
</td>
<td>
2.78
</td>
<td>
2.88
</td>
<td>
2.78
</td>
</tr>
<tr>
<td>
c
</td>
<td>
120.5
</td>
<td>
121.7
</td>
<td>
120.5
</td>
<td>
121.7
</td>
</tr>
<tr>
<td>
d
</td>
<td>
1.39
</td>
<td>
1.38
</td>
<td>
1.39
</td>
<td>
1.38
</td>
</tr>
</table>

====QST2 and QST3====

As well as being able to set up a guess geometry of a transition state,and optimise to it using the two methods above, we can also carry out a QST2 calculation, whereby we interpolate between starting material and product, to locate the transition state along that path. This is what we shall attempt to do here, for the boat transition state

We shall take out Anti-2 C<sub>i</sub> 1,5-Hexadiene Conformer. As we saw, this is not the lowest energy conformer, but is only ca. 0.5 kcalmol<sup>-1</sup> higher in energy, so is very thermally accessible. We are going to take this conformer because, as we shall see, it has symmetry about a point, and when we set the dihedral, to come, about a plane, so the interpolation will be easier, and hence less computationally expensive and more likley to work

A necessary condition for QST2 is that the order of atoms in the reactant input metches that in the product input. Because the reactant and product are the same molecule, but a different order of atoms, our first task is to create a molgroup, with two frames of the same stutcure, then renumber the second frame accordingly, so that when the molecule rearranges via a [3,3] shift, the order is the same. Once this was done, a HF 3-21G QST2 calculation was carried out. This job however, failed and produced an erronious geometry. This is because the simple interpolation moved atoms about, but looking at the geometries, we can easily see that to be able to get to the transition sate, the C<sub>i</sub> anti structure clearly needs first to rotate about the central C-C. We then took the starting geometries from the failed QST2 job, and set the central C<sub>4</sub> dihedral to 0<sup>o</sup>. Then the two halves of the molecule were brought closer together by setting internal bond angles to both be 100<sup>o</sup>. This structure has symmetry about a plane passing across the centre of the molecule, hence, when we interpolate between the two, we should find the boat transition state, since it also has that plane-symmetry. The calculation was rerun from these starting geometries.

<table border='1'>
<tr>
<td colspan='2'>
''' Boat QST2 TS Optimisation start and end points: Failed job'''
</td>
<td rowspan='3'>
</td>
<td colspan='2'>
''' Boat QST2 TS Optimisation start and end points: Rotated Dihedral'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Start Point
</td>
<td>
End Point
</td>
</tr>
<tr>
<td>
[[Image:pm08Anti2QST2start.png|200px]]
</td>
<td>
[[Image:pm08Anti2QST2end.png|200px]]
</td>
<td>
[[Image:pm08Antirotated2QST2start.png|200px]]
</td>
<td>
[[Image:pm08Antirotated2QST2end.png|200px]]
</td>
</tr>
</table>

The result is indeed that expected - the boat transition state. Again, when we compare the resulting structural parameters to those listed above, we find them to be the same.

For more complex jobs, it is possible to specify a guess structure for the transition state - for example, here we could place in the guesses from above. This would then be a QST3 calculation. However, here it will be unnecessary, since some though as to the starting geometry emabld us to quickly find the transition state.

===Following the reaction pathway: IRC===
[[Image:pm08CopeChairIRC.png|700px|right]]

[[Image:pm08CopeBoatIRC.png|700px|right]]

[[Image:pm08Coperelativeenergy.png|700px|right]]

We have found chair and boat transition structures for the Cope rearrangement of 1,5-Hexadiene. Now we need to determine which starting conformation is necessary to reach those transition states. To do this, we use the Intrisic Reaction Coordinate method. Here, we start at the geometry of our chosen transiton state to investigate, and we choose to follow the reaction path as the energy decreases down to a minimum geometry - we are following the reaction coordinate in an energy profile plot. In ths case of the Cope rearragment, the profile will be symmetrical about the transntion state (same molecule and conformation) but usually products have lower energy than reactants, hence, we usually follow the path in both directions but here we only have to go in one direction.

From the optimised geometry of the transition state, taken from the results of the Berny Optimisation (althogh as we saw the other methods gave the same structure), an IRC calculation was carried out, to follow the forward direction, with a maximum number of points set to 200, and specifying that the force constants be calculated at every step. Because we set the calculation to see if we have reached a minimum at every step, we don't risk not finding the true minimum. It doesn't take 200 steps to run, the aim of this was to allow the calculation to find the minimum without risking it not reaching it.

If we observe the strctures of the final IRC geometry, we can judge which conformer the reaction proceeds from. From the Chair-TS IRC results, we find that the Gauche-2 confomation gives the necessary orientation for this rearrangement. The boat form however converges to a staggered form, which as we know is itself a transition state between lower energy gauche and/or anti conformations. This first seems to sugest the IRC failed, but if we consider that the caluclation finds the nearest minimum in the give direction, then this condition is fulfilled by a transition state - just the wrong type. Then, to find the nearest stable conformer, we can run another IRC on the resulting staggered geometry. Doing this, we find the calculation converges to the Gauche-3 conformer, by rotation by 60<sup>o</sup> of the central C-C bond.

These two starting conformations are, as we saw, not the lowest energy conformers. However, all the conformers, and the transition states between them were thermally accessible, i.e this system did not exhibit atropisomerism, taking an ensemble average of the system we would find a certain proportion of the molecules to be in each state, with smaller proportions for higher energy conformations.

We also see, by plotting together the energy difference between reactant and product for the two pathways, we find that the boat transition state is higher in energy than the chair transition state on the pathway between their respective conformations to allow reaction.

To be able to report a calculated activation energy for the reaction, we first need to reoptimise our transition structures to DFT B3LYP 6/31G* theory, and compare their energies to that of the Anti-1 conformer, since by convention the activation energy is reported relative to the lowest energy conformer. The activation energy between chair TS and Anti-1 Conformer is cauclated to be 34.4 kcalmol<sup>-1</sup>. The experimentally determined value is 33.5±0.5kcalmol<sup>-1</sup>. The activation energy between boat TS and Anti-1 Conformer is calculated to be 43.1 kcalmol<sup>-1</sup>. The experimentally determined value is 44.7±0.2 kcalmol<sup>-1</sup>. These are at 0K. The values are very close to those from experiment, showing the power of these computational methods.

</div>
----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T12:02:12Z

Pm08: /* The Diels Alder Cycloaddition between Butadiene and Ethene */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a π<sub>4</sub>s + π<sub>2</sub>s cycloaddition between a diene and a dienophile, to form two new σ bonds from the termini of a conjugated π system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry propoerties of the Frontier orbitals of the reactants, we will show that this reactio is allowed, and make a prediciton as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transiiton state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloaditon between Maleic anhydride acting ad the dienophile and 1,3-Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reacting. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations. Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal π system, featuring a π homo and π* LUMO. The HOMO is symmetric with respect to a plane bisecting the molecule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a π system, with equal coefficients on both π orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the π* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new σ bonds, if one is empty and one is filled. Becuase of the symmetry constraint, the geomerty of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from pi bonds, we have to rehybridise sp<sup>2</sup> to sp<sup>3</sup>, and we require the π bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combination of FOs , above. We couldn't make a guess as to which case we have without calculation, because these are both fairly 'electronically neutral' alkenes, i.e no electron pushing or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene π bond forming, and the ethene π bond and cis-butadiene π bonds breaking, with increasing electron density in between the two molecules, where the sigma bonds are forming.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinsaions.

==Optimising reactants and product==

Compared to the Cope rearrangement, the Diels Alder reaction is Bi-molecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32Å.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minim and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5o intervals, ie a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomolous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90<sup>o</sup>, and a maximum in the energy profile, 7.56 kcalmol<sup>-1</sup> higher in energy than the trans conformer. At 90<sup>o</sup> apart, the π systems are orthogonal, so there can be no conjugation whatsoever. At 0<sup>o</sup>, the two pi systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130<sup>o</sup>, which is 3.54 kcalmol<sup>-1</sup> higher in energy than the trans conformer. In this case, we have a balance of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stornger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is in fact a transition state, not a stable conformer, and is 3.88 kcalmol<sup>-1</sup> higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130<sup>o</sup>-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90<sup>o</sup>-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyclohexane conformation, we can make some educated guesses as to what will be the stable minima, then we shall test our predictions by optimising to try to find these structures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposed by the double bond, we can imagine two minimum conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A half boat structure was created by taking a bicyclo system, and removing one CH<sub>2</sub>CH<sub>2</sub> group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol<sup>-1</sup>.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels ALder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST 2 calcualtion interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labelling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the pi system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to reoptimiseour HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol-1. The calculated free eneergy change of reaction is -43.1 kcalmol-1.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79362

2010-12-17T11:53:59Z

Pm08: /* Following the reaction pathway: IRC */

=The Cope Rearrangement=
<div align='justify'>
[[Image:pm08copescheme.png|frame|The Cope Rearrangement, a [3,3]-Sigmatropic alkyl shift]]
The Cope Rearrangement involves a concerted [3,3]-Sigmatropic alkyl shift in a 1,5-diene system. The reaction proceeds thermally, via a Huckel topography, with Suprafacial sterochemistry. We are going to show this statement to be true, by using computational methods to study this reaction.

In the most simple case of a Cope reaction, 1,5-hexadiene rearranges. The product is the same as the reactant, but with the order of the atoms changed. We shall initially investigate this reaction, first looking at the geometry of 1,5-hexadiene to determine the most stable conformer, and why, and then explore various methods of optimising the transition state of the reaction.

==The Cope Rearrangement of 1,5-Hexadiene==
===Optimising the Geometry of 1,5-Hexadiene===

[[Image:pm0815hexadiene.png|left]]
Initially, we shall optimise a molecule of 1,5-Hexadiene, exploring the geometries of different conformations, asking why certain conformations are lower in energy than others.

Using the Gaussview 3.09 GUI, a molecule of 1,5-hexadiene was created, with anti-stereochemistry across the central C-C bond (the Dihedral angle was set to 180<sup>o</sup>). This was optimised using the HF/3-21G Level of theory. The calculation optimised the molecule to a C<sub>2</sub>-symmetric geometry, with energy -231.69260 Eh = -145389.42 kcalmol<sup>-1</sup>. This corresponds to the Anti-1 geometry listed in appendix 1.<ref name='one'>[[Mod:phys3#Appendix_1]]</ref> According to appendix 1, we have found the lowest energy conformation of anti-1,5-hexadiene.

Next, a molecule of gauche-1,5-hexadiene was created (the Dihedral angle across the central C-C set to 60<sup>o</sup>). An optimisation was again run, using the same level of theory. The optimised geometry was again C<sub>2</sub>-symmetric, with an energy of -231.69167 Eh = -145388.84 kcal mol<sup>-1</sup>. The energy of this gauche conformation, corresponding to Gauche-2 in appendix 1<ref name='one'>[[Mod:phys3#Appendix_1]]</ref>, was 0.59Kcalmol<sup>-1</sup> higher in energy than the Anti-1 conformation we first optimised to. Why was this conformation higher in energy than the anti conformation?<ref name='rzepa'>http://www.ch.ic.ac.uk/local/organic/conf/</ref>

[[Image:pm08antigauchesigmaenergy.png|left]]
We need to consider the favorable secondary orbital overlap between σ/σ* orbitals in anti-relationships. Both conformations are staggered, so every bond has an anti-relationship to another bond. In the anti-conformer, if we look at those relationships, we see we have 2σ<sub>CC</sub>/σ<sub>CC</sub>* and 4σ<sub>CH</sub>/σ<sub>CH</sub>*. In the gauche-conformer, we now have 2σ<sub>CC</sub>/σ<sub>CH</sub>*, 2σ<sub>CH</sub>/σ<sub>CC</sub>* and 2σ<sub>CH</sub>/σ<sub>CH</sub>*. We can draw up a qualitative energy level diagram showing E<sub>2</sub> stabilising secondary interaction between orbitals, to explain the preference for the anti-conformation.

First, we define the position of the CC and CH σ and σ* orbitals. We know that the σ<sub>CC</sub> is lower in energy than the σ<sub>CH</sub>, because the two C sp<sup>3</sup> orbitals are equal in energy, so are split more than a CH pair, because the C sp<sup>3</sup> and H s orbital are apart in energy. The same is true for the σ* orbitals. In the anti conformation, the secondary overlap between σ<sub>CC</sub>/σ<sub>CC</sub>* produces a stabilisation. Likewise for the σ<sub>CH</sub>/σ<sub>CH</sub>* overlap. We would expect the σ<sub>CC</sub>/σ<sub>CC</sub>* overlap to be slightly more stabilising than the σ<sub>CH</sub>/σ<sub>CH</sub>* stabilisation, because the σ/σ* gap would be less, because the C FO's atoms are more evenly matched in energy. In the gauche-conformer, we also have the σ<sub>CH</sub>/σ<sub>CH</sub>* overlap, but now no σ<sub>CC</sub>/σ<sub>CC</sub>* overlap. Instead we have σ<sub>CC</sub>/σ<sub>CH</sub>* overlap, which is very little stabilising, because the orbitals are far apart in energy, and a σ<sub>CH</sub>/σ<sub>CC</sub>* overlap, which is more stabilising than the σ<sup>CH</sup>/σ<sub>CH</sub>* overlap, because the orbitals are closer in energy. Adding up the total number of interactions, we would expect the anti-conformer to be lower in energy, because, overall, the overlap of HOMO σ/σ* pairs will be more stabilising that the overlap of HOMO and HETRO σ/σ* pairs. This agrees with the resulting energy from calculation.

However, we also need to consider interactions between non-bonded pairs of atoms - The van der Waals interaction. This is the anisotropic interaction between two non-bonded atoms separated by a distance r. If r is very small, then the interaction is repulsive, due to n/n and e/e repulsions. If r is large, then the atoms are too far to be influenced. If r however is ideal, then the stabilising n/e Coulombic interaction is balanced by n/n and e/e and overall we have a lower energy. This is the sum of the two van der Waals radii of the atoms involved. Even if the distance is slightly larger than this distance though, the interaction is still attractive, since this is over a large range. If we inspect the anti and gauche conformers, we see that the Gauche conformer sets up more of these interactions by folding in on itself. However, as we have seen, overall, the energy of the anti conformer is lower, but not by a great deal.

Based on what we have just said, we could imagine a lower energy gauche-conformer. If in the current gauche conformer, one CH<sub>2</sub>CH group twisted 180<sup>o</sup>, then one H atoms is moved within the molecule somewhat, and into the attractive region of more carbon and hydrogen atoms. Also, this twist means the two 'halves' of the molecule are not not directly over each other in space - before, they were, but they were far away, so steric bumping is unlikely, but may make a slight repulsive contribution. This has however now been removed. We took the gauche-conformation, twisted a CH<sub>2</sub>CH group by 180<sup>o</sup>, and then optimised to HF/3-21G level of theory, and the resulting energy was -231.69266 Eh = -145389.46 kcalmol<sup>-1</sup>. The resulting geometry was C<sub>1</sub>-symmetric, corresponding to Gauche 3 in Appendix 1<ref name='one'>[[Mod:phys3#Appendix_1]]</ref>. This is 0.62 kcalmol<sup>-1</sup> more stable than the other Gauche conformer, by virtue of extra attractive van der Waals interactions. Also, this is 0.036 kcalmol<sup>-1</sup> more stable than the anti conformer. This is surprising, showing that the van der Waals interactions do make a significant contribution to the energy of the molecule, and in this case, overall, the energy is lower, by a small amount. However, in the Gauche conformers, we saw we have many van der Waals interactions, whereas in the anti conformer, we had few, so we can say overall, that on the anti-conformer, the σ/σ* is greater than in the gauche-conformers.

We should also be able to imagine another low-energy conformation of the anti-geometry. In Anti-1, the CH<sub>2</sub>CH groups are both twisted the same way with respect to the central anti-linkage, resulting in C<sub>2</sub> symmetry. Above, we twisted one group and found a lower energy gauche conformer. Let's do the same now. Twisting one CH<sub>2</sub>CH group and optimising to HF/3-21G resulted in a C<sub>i</sub>-symmetric geometry with energy -231.692535 Eh = -145389.38 kcalmol<sup>-1</sup>, corresponding to Anti-2 in appendix 1<ref name='one'>[[Mod:phys3#Appendix_1]]</ref>. This is 0.042 kcalmol<sup>-1</sup> higher in energy than the Anti-1 conformer. In this case, twisting of the group did not result in a lower energy conformer.

<table border='1'>
<tr>
<td colspan='5'>
'''1,5-Hexadiene Conformers /HF 3-21G'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Anti-1'''
</td>
<td>
'''Anti-2'''
</td>
<td>
'''Gauche-2'''
</td>
<td>
'''Gauche-3'''
</td>
</tr>
<tr>
<td valign='top'>
'''Geometry'''
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Anti-1</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copeanti1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Anti-2</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copeanti2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Gauche-2</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copegauche2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Gauche-3</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copegauche3.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td>
'''Energy /Eh'''
</td>
<td>
-231.69260
</td>
<td>
-231.69254
</td>
<td>
-231.69167
</td>
<td>
-231.69266
</td>
</tr>
<tr>
<td>
'''Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
0.036
</td>
<td>
0.078
</td>
<td>
0.62
</td>
<td>
0.0
</td>
</tr>
</table>

Let us make a comparison between different levels of theory. Above, we used HF/3-21G. Now, we are going to take our low-energy conformer, listed in the table above and re-optimise, using DFT/B3LYP/6-31G*. We shall also carry out a frequency analysis for these geometries, to verify that we have indeed reached a minimum.

<table border='1'>
<tr>
<td colspan='7'>
'''Comparison between levels of theory in the optimisation of 1,5-Hexadiene'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''HF 3-21G Energy /Eh'''
</td>
<td>
'''DFT B3LYP 6-31G* Energy /Eh'''
</td>
<td>
'''Difference /Eh'''
</td>
<td>
'''HF 3-21G Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
'''DFT B3LYP 6-31G* Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
'''Imaginary modes /cm<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''Anti-1 (C<sub>2</sub>)'''
</td>
<td>
-231.69260
</td>
<td>
-234.61180
</td>
<td>
2.91920
</td>
<td>
0.036
</td>
<td>
0.0
</td>
<td>
-8.41

-3.82
</td>
</tr>
<tr>
<td>
'''Anti-2 (C<sub>i</sub>)'''
</td>
<td>
-231.69254
</td>
<td>
-234.61172
</td>
<td>
2.91902
</td>
<td>
0.078
</td>
<td>
0.052
</td>
<td>
-6.20
</td>
</tr>
<tr>
<td>
'''Gauche-2 (C<sub>2</sub>)'''
</td>
<td>
-231.69167
</td>
<td>
-234.61069
</td>
<td>
2.91867
</td>
<td>
0.62
</td>
<td>
0.70
</td>
<td>
-13.97

-13.36

-11.10
</td>
</tr>
<tr>
<td>
'''Gauche-3 (C<sub>1</sub>)'''
</td>
<td>
-231.69266
</td>
<td>
-234.61133
</td>
<td>
2.91918
</td>
<td>
0.0
</td>
<td>
0.30
</td>
<td>
-4.40
</td>
</tr>
</table>

Between the two sets of theory, we see that the higher level DFT method has calculated a different relative energy order of our conformers. The two levels of theory do however give the same order of stabilities between the pairs of anti- and gauche- conformers, so this suggests that the DFT calculated a greater σ/σ* stabilising interaction, or a weak vdW stabilising interaction. Hence, the gauche are calculated to be less stable than the anti conformers under DFT/B3LYP/6-31G*.

There is however, a slightly worrying result when we look at the imaginary frequencies. These should all be zero, if we have indeed optimised to a minimum. I think perhaps using this mid level basis set, that the geometry hasn't quite reached the minimum. Because the energy differences are very small between conformers, a slight difference in geometry could lead us to an incorrect order of relative energies. Hence, the optimisation was rerun again, from the DFT result, this time specifying very tight convergance criteria, and int=ultrafine This is computationally expensive, but I think it is necessary to establish which is the lowest energy conformer. The results:

<table border='1'>
<tr>
<td colspan='4'>
'''DFT B3LYP 6-31G* Very tight optimisation 1,5-Hexadiene Conformers'''
</td>
</tr>
<tr>
<td>
'''Anti-1 (C<sub>2</sub>)'''
</td>
<td>
-234.61179
</td>
<td>
0.0
</td>
<td>
-6.6

-3.2
</td>
</tr>
<tr>
<td>
'''Anti-2 (C<sub>i</sub>)'''
</td>
<td>
-234.61171
</td>
<td>
0.051
</td>
<td>
-5.6

-1.9
</td>
</tr>
<tr>
<td>
'''Gauche-2 (C<sub>2</sub>)'''
</td>
<td>
-234.61070
</td>
<td>
0.68
</td>
<td>
-5.8

-5.4

-4.2
</td>
</tr>
<tr>
<td>
'''Gauche-3 (C<sub>1</sub>)'''
</td>
<td>
-234.61133
</td>
<td>
0.29
</td>
<td>
-0.0004
</td>
</tr>
</table>

This very tight convergence reduced the magnitude of all of the imaginary modes, showing the geometry is moving toward the bottom of the potential well. The key result here is that the energy changed only by ~0.01 kcalmol<sup>-1</sup>, and the order of conformers did not change. If we consider the potential surface for this molecule, we expect wells for the conformers we have found. For the two pairs of anti and gauche conformers, the geometry difference is not a great deal, to the wells are close, and probably not very deep between them. Hence, this may also explain why we get small imaginary frequencies – we are not at a transition structure, but in a shallow well, not quite at the bottom. Because this result agrees with that for the quicker calculation, we shall use the DFT B3LYP 6-31G* theory for further analysis.

[[Image:pm08anti2thermochemistry.png|right]]
The energies reported are for the conformations at 0K. Carrying out a frequency analysis allows us to make a correction to other temperatures, specified using a readisotopes keyword. Using the Anti-2 conformer, we are going to invetsigate the effect of increasing temperature on the energy of the system, taking into account the thermal correction, by calcuating the thermal corretion at a range of temperatures, by specifying a frwquency calculation to the DFT B3LYP 6-31G* level, with the readisotopes tag, on a DFT B3LYP 6-31Gd optimised geometry, and then plotting the resulting Sum of Electronic, ZPE and thermal energies.

We initially see that at low temperatures, the energy is increasing, at an increasing rate with increasing temperature, until a point where the increase in energy of the system is linear with temperature. At T=0k, all the molecules are in their vibrational ground state. As T is rasied, but kept low, the first few vibrationally excited states begin to be populated. Increasing the thermal energy further will populate more states until it gets to a point where all the vibrational states are filled. In this regime, we see an increasing reat of change of energy with tempeture. At this point, the discrete proporties of the molecules can be treated classically, i.e the vibrational temperature. After this temperature is surpassed, the molecule bahaves classically, and its increase in energy is linear with temperature.

===Locating the Transition State Structures===

[[Image:pm08copechairboatts.png|left]]
We are going to use a variety of methods to explore the transition state geometries of this rearrangement. Initially, we shall form a guess, consisting of two allyl fragments separated in space, with the correct symmetry to hopefully optimise to the transition structure. We shall use the Berny TS method to optimise, and also the 'Frozen' Coordinate, two-stage optimisation method. Then, we shall use the QST2 method, now, not forming a transition state guess, but interpolating between the starting material and product.

If we consider two allyl fragments separated in space, we can form two potential transition state structures, corresponding to chair and boat cyclohexyl-like geometries. We shall explore both reaction pathways, via chair and boat TS structures, to determine which is the lower energy, and hence more favorable process.

====Berny Optimisation====
[[Image:pm08copetsguesses.png|right]]
Using Gaussview 3.09 GUI, an allyl, C<sub>3</sub>H<sub>5</sub>, fragment was created. This was optimised using HF 3-21G theory, and the resulting geometry was then used to build our transition state guesses. Two of these fragments were placed face on, one overlapping directly, to give a C2v-symmetric geometry - Boat, and once with one fragment rotated, with a terminal C overlapping with terminal H on the other fragment, to give a C2h-symmetric geometry - Chair. The two allyl fragments were set 2.2A apart in both starting guesses.

These structures were then optimised to a Transition State, using the Berny method and HF/3-21G theory, calculating the force constants once. The resulting geometries are shown below. In both structures, the central C atom of the allyl fragments pucker away from the other fragment slightly. In the chair C2h structure, the terminal C atoms are separated by 2.02A. In the C2v boat, they are separated by 2.14A.

<table border='1'>
<tr>
<td colspan='2'>
'''HF 3-21G TS(Berny) Opt results'''
</td>
</tr>
<tr>
<td>
Chair-C2h
</td>
<td>
Boat-C2v
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Cope Chair TS Benry Optimisation result</title><color>white</color><size>150</size>
<script>rotate; measure 1 10;</script>
<uploadedFileContents>pm08copechairtsberny.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Cope Boat TS Benry Optimisation result</title><color>white</color><size>150</size>
<script>rotate; measure 1 10;</script>
<uploadedFileContents>pm08copeboattsberny.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Note that although Jmol draws these as propene fragments, the two C-C bond lengths in each fragment are equal and they are in reality allyl like. How do we know these are transition states? We look for one imaginary mode, corresponding to the displacement either side of the transition state. In the Chair-C<sub>2</sub>h TS, we find exactly that, an imaginary frequency with magnitude 817cm<sup>-1</sup>. Likewise, in the Boat-C<sub>2</sub>v TS, at -840cm-1. Animating these imaginary modes, we see each allyl fragment bend back and forth from each other. This is the Cope rearrangement.

<table border='1'>
<tr>
<td colspan='2'>
'''HF 3-21G TS(Berny) Opt Imaginary modes'''
</td>
</tr>
<tr>
<td>
'''Chair-C<sub>2</sub>h'''
</td>
<td>
'''Boat-C<sub>2</sub>v'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Cope Chair TS Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 3;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834132.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Cope Boat TS Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 3;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834131.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td>
-817cm<sup>-1</sup>
</td>
<td>
-840cm<sup>-1</sup>
</td>
</tr>
</table>

====Frozen Coordinate Optimisation====

The transition state structure guesses were taken and using the redundant coordinate tool in Gaussview, the terminal C atoms of the two fragments were frozen, at a set distance of 2.2Å apart. What this does is fix the position of these atoms when we optimise the structure. We carried out a HF/3-21G Opt=Modredundant calculation. In the resulting geometry, the central C atoms had puckered out slightly, as they did above, but as we said, the terminal atoms stayed fixed. Then we took this resulting geometry and optimised again, using the same theory, this time without the condition of being fixed, but to differentiate along the forming and breaking bonds to find the transition state. The value in this method is that we do not have to calculate force constants, which for large jobs will be less computationally expensive.

How do these compare to the Berny Results? If we measure the following geometric parameters, in both the chair and boat structures for both optimisation methods, we find them to be be identical to 0.01Å and 0.1<sup>o</sup>. Hence, we can say that for this simple system, both methods of optimising a transition state from a guess are equally valid.

<table border='1'>
<tr>
<td colspan='5'>
'''Comparing Optimised TS structures for two different methods'''
</td>
</tr>
<tr>
<td colspan='5'>
[[Image:pm08guesstscompare.png]]
</td>
</tr>
<tr>
<td rowspan='2'>
'''Parameter'''
</td>
<td colspan='2'>
'''HF 3-21G Berny TS Optimisation'''
</td>
<td colspan='2'>
'''HF 3-21G Frozen Coordinate TS Optimisation'''
</td>
</tr>
<tr>
<td>
Chair
</td>
<td>
Boat
</td>
<td>
Chair
</td>
<td>
Boat
</td>
</tr>
<tr>
<td>
a
</td>
<td>
2.02
</td>
<td>
2.14
</td>
<td>
2.02
</td>
<td>
2.14
</td>
</tr>
<tr>
<td>
b
</td>
<td>
2.88
</td>
<td>
2.78
</td>
<td>
2.88
</td>
<td>
2.78
</td>
</tr>
<tr>
<td>
c
</td>
<td>
120.5
</td>
<td>
121.7
</td>
<td>
120.5
</td>
<td>
121.7
</td>
</tr>
<tr>
<td>
d
</td>
<td>
1.39
</td>
<td>
1.38
</td>
<td>
1.39
</td>
<td>
1.38
</td>
</tr>
</table>

====QST2 and QST3====

As well as being able to set up a guess geometry of a transition state,and optimise to it using the two methods above, we can also carry out a QST2 calculation, whereby we interpolate between starting material and product, to locate the transition state along that path. This is what we shall attempt to do here, for the boat transition state

We shall take out Anti-2 C<sub>i</sub> 1,5-Hexadiene Conformer. As we saw, this is not the lowest energy conformer, but is only ca. 0.5 kcalmol<sup>-1</sup> higher in energy, so is very thermally accessible. We are going to take this conformer because, as we shall see, it has symmetry about a point, and when we set the dihedral, to come, about a plane, so the interpolation will be easier, and hence less computationally expensive and more likley to work

A necessary condition for QST2 is that the order of atoms in the reactant input metches that in the product input. Because the reactant and product are the same molecule, but a different order of atoms, our first task is to create a molgroup, with two frames of the same stutcure, then renumber the second frame accordingly, so that when the molecule rearranges via a [3,3] shift, the order is the same. Once this was done, a HF 3-21G QST2 calculation was carried out. This job however, failed and produced an erronious geometry. This is because the simple interpolation moved atoms about, but looking at the geometries, we can easily see that to be able to get to the transition sate, the C<sub>i</sub> anti structure clearly needs first to rotate about the central C-C. We then took the starting geometries from the failed QST2 job, and set the central C<sub>4</sub> dihedral to 0<sup>o</sup>. Then the two halves of the molecule were brought closer together by setting internal bond angles to both be 100<sup>o</sup>. This structure has symmetry about a plane passing across the centre of the molecule, hence, when we interpolate between the two, we should find the boat transition state, since it also has that plane-symmetry. The calculation was rerun from these starting geometries.

<table border='1'>
<tr>
<td colspan='2'>
''' Boat QST2 TS Optimisation start and end points: Failed job'''
</td>
<td rowspan='3'>
</td>
<td colspan='2'>
''' Boat QST2 TS Optimisation start and end points: Rotated Dihedral'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Start Point
</td>
<td>
End Point
</td>
</tr>
<tr>
<td>
[[Image:pm08Anti2QST2start.png|200px]]
</td>
<td>
[[Image:pm08Anti2QST2end.png|200px]]
</td>
<td>
[[Image:pm08Antirotated2QST2start.png|200px]]
</td>
<td>
[[Image:pm08Antirotated2QST2end.png|200px]]
</td>
</tr>
</table>

The result is indeed that expected - the boat transition state. Again, when we compare the resulting structural parameters to those listed above, we find them to be the same.

For more complex jobs, it is possible to specify a guess structure for the transition state - for example, here we could place in the guesses from above. This would then be a QST3 calculation. However, here it will be unnecessary, since some though as to the starting geometry emabld us to quickly find the transition state.

===Following the reaction pathway: IRC===
[[Image:pm08CopeChairIRC.png|700px|right]]

[[Image:pm08CopeBoatIRC.png|700px|right]]

[[Image:pm08Coperelativeenergy.png|700px|right]]

We have found chair and boat transition structures for the Cope rearrangement of 1,5-Hexadiene. Now we need to determine which starting conformation is necessary to reach those transition states. To do this, we use the Intrisic Reaction COOrdinat method. Here, we start at the geometry of our chosen transiton state to invensitgae, and we choose to follow the reaction path as the energy decreases down to a minimum geometry - we are following the reaction coordinate in an energy profile plot. In ths case of the Cipe rearragment, the profile will be symmetrucal about the transntion state (same molecule and conformation) but usually products have lower energy than reactants, hence, we usually follow the path in both directions but here we only have to go in one direction.

From the optimised geometry of the transition state, taken from he results of the Berny Optimisation (althogh as we saw the other methods gave the same structure), an IRC calculation was carried out, to follow the forward direction, with a maximum number of points set to 200, and specifying that the force constants be calculated at every step. Because we set the calculation to see if we have reached a minimum at every step, we don't risk not finding the true minimum.

If we observe the strctures of the final IRC geometry, we can judge which conformer the reaction proceeds from. From the Chair-TS IRC results, we find that the Gauche-2 confomation gives the necessary orientation for this rearrangement. The boat form however converges to a staggered form, which as we know is itself a transition state between lower energy gauche and/or anti conformations. This first seems to sugest the IRC failed, but if we consider that the caluclation finds the nearest minimum in the give direction, then thsi condition is fulfilled by a transition state - just the wrong type. Then, to find the nearest stable conformer, we can run another IRC on the resulting staggered geometry. Doing this, we find the calculation converges to the Gauche-3 conformer, by rotation by 60o of the central C-C bond.

These two starting conformations are, as we saw, not the lowest energy conformers. However, all the conformers, and the transition states between them were thermally accessible, i.e this system did not exhibit atropisomerism, taking an ensemble average of the system we would find a certain proportion of the molecules to be in each state, with smaller proportions for higher energy conformations.

We also see, by plotting together the energy difference between reactant and product for the two pathways, we find that the boat transition state is higher in energy than the chair transition state on the pathway between their respective conformations to allow reaction.

To be able to report a calculated activation energy for the reaction, we first need to reoptimise our transition structures to DFT B3LYP 6/31G* theory, and compare their energies to that of the Anti-1 conformer, since by convention the activation energy is reported relative to the lowest energy conformer. The activation energy between chair TS and Anti-1 Conformer is cauclated to be 34.4 kcalmol-1. The experimentally determined value is 33.5±0.5kcalmol-1. The activation energy between boat TS and Anti-1 Conformer is calculated to be 43.1 kcalmol-1. The experimentally determined value is 44.7±0.2 kcalmol-1. These are at 0K, so I assume the experimental values are extrapolations of higher T data, hence the error. We find our two values to be very close to those predicted,

</div>
----
<div class="references-small">
<references/>
General references made throughout to:

M.Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3, 2008

J.B.Foresman and A.Frisch, Exploring Chemistry with Electronic Structure Methods, 1996

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79362

2010-12-17T11:50:57Z

Pm08: /* Optimising the Geometry of 1,5-Hexadiene */

=The Cope Rearrangement=
<div align='justify'>
[[Image:pm08copescheme.png|frame|The Cope Rearrangement, a [3,3]-Sigmatropic alkyl shift]]
The Cope Rearrangement involves a concerted [3,3]-Sigmatropic alkyl shift in a 1,5-diene system. The reaction proceeds thermally, via a Huckel topography, with Suprafacial sterochemistry. We are going to show this statement to be true, by using computational methods to study this reaction.

In the most simple case of a Cope reaction, 1,5-hexadiene rearranges. The product is the same as the reactant, but with the order of the atoms changed. We shall initially investigate this reaction, first looking at the geometry of 1,5-hexadiene to determine the most stable conformer, and why, and then explore various methods of optimising the transition state of the reaction.

==The Cope Rearrangement of 1,5-Hexadiene==
===Optimising the Geometry of 1,5-Hexadiene===

[[Image:pm0815hexadiene.png|left]]
Initially, we shall optimise a molecule of 1,5-Hexadiene, exploring the geometries of different conformations, asking why certain conformations are lower in energy than others.

Using the Gaussview 3.09 GUI, a molecule of 1,5-hexadiene was created, with anti-stereochemistry across the central C-C bond (the Dihedral angle was set to 180<sup>o</sup>). This was optimised using the HF/3-21G Level of theory. The calculation optimised the molecule to a C<sub>2</sub>-symmetric geometry, with energy -231.69260 Eh = -145389.42 kcalmol<sup>-1</sup>. This corresponds to the Anti-1 geometry listed in appendix 1.<ref name='one'>[[Mod:phys3#Appendix_1]]</ref> According to appendix 1, we have found the lowest energy conformation of anti-1,5-hexadiene.

Next, a molecule of gauche-1,5-hexadiene was created (the Dihedral angle across the central C-C set to 60<sup>o</sup>). An optimisation was again run, using the same level of theory. The optimised geometry was again C<sub>2</sub>-symmetric, with an energy of -231.69167 Eh = -145388.84 kcal mol<sup>-1</sup>. The energy of this gauche conformation, corresponding to Gauche-2 in appendix 1<ref name='one'>[[Mod:phys3#Appendix_1]]</ref>, was 0.59Kcalmol<sup>-1</sup> higher in energy than the Anti-1 conformation we first optimised to. Why was this conformation higher in energy than the anti conformation?<ref name='rzepa'>http://www.ch.ic.ac.uk/local/organic/conf/</ref>

[[Image:pm08antigauchesigmaenergy.png|left]]
We need to consider the favorable secondary orbital overlap between σ/σ* orbitals in anti-relationships. Both conformations are staggered, so every bond has an anti-relationship to another bond. In the anti-conformer, if we look at those relationships, we see we have 2σ<sub>CC</sub>/σ<sub>CC</sub>* and 4σ<sub>CH</sub>/σ<sub>CH</sub>*. In the gauche-conformer, we now have 2σ<sub>CC</sub>/σ<sub>CH</sub>*, 2σ<sub>CH</sub>/σ<sub>CC</sub>* and 2σ<sub>CH</sub>/σ<sub>CH</sub>*. We can draw up a qualitative energy level diagram showing E<sub>2</sub> stabilising secondary interaction between orbitals, to explain the preference for the anti-conformation.

First, we define the position of the CC and CH σ and σ* orbitals. We know that the σ<sub>CC</sub> is lower in energy than the σ<sub>CH</sub>, because the two C sp<sup>3</sup> orbitals are equal in energy, so are split more than a CH pair, because the C sp<sup>3</sup> and H s orbital are apart in energy. The same is true for the σ* orbitals. In the anti conformation, the secondary overlap between σ<sub>CC</sub>/σ<sub>CC</sub>* produces a stabilisation. Likewise for the σ<sub>CH</sub>/σ<sub>CH</sub>* overlap. We would expect the σ<sub>CC</sub>/σ<sub>CC</sub>* overlap to be slightly more stabilising than the σ<sub>CH</sub>/σ<sub>CH</sub>* stabilisation, because the σ/σ* gap would be less, because the C FO's atoms are more evenly matched in energy. In the gauche-conformer, we also have the σ<sub>CH</sub>/σ<sub>CH</sub>* overlap, but now no σ<sub>CC</sub>/σ<sub>CC</sub>* overlap. Instead we have σ<sub>CC</sub>/σ<sub>CH</sub>* overlap, which is very little stabilising, because the orbitals are far apart in energy, and a σ<sub>CH</sub>/σ<sub>CC</sub>* overlap, which is more stabilising than the σ<sup>CH</sup>/σ<sub>CH</sub>* overlap, because the orbitals are closer in energy. Adding up the total number of interactions, we would expect the anti-conformer to be lower in energy, because, overall, the overlap of HOMO σ/σ* pairs will be more stabilising that the overlap of HOMO and HETRO σ/σ* pairs. This agrees with the resulting energy from calculation.

However, we also need to consider interactions between non-bonded pairs of atoms - The van der Waals interaction. This is the anisotropic interaction between two non-bonded atoms separated by a distance r. If r is very small, then the interaction is repulsive, due to n/n and e/e repulsions. If r is large, then the atoms are too far to be influenced. If r however is ideal, then the stabilising n/e Coulombic interaction is balanced by n/n and e/e and overall we have a lower energy. This is the sum of the two van der Waals radii of the atoms involved. Even if the distance is slightly larger than this distance though, the interaction is still attractive, since this is over a large range. If we inspect the anti and gauche conformers, we see that the Gauche conformer sets up more of these interactions by folding in on itself. However, as we have seen, overall, the energy of the anti conformer is lower, but not by a great deal.

Based on what we have just said, we could imagine a lower energy gauche-conformer. If in the current gauche conformer, one CH<sub>2</sub>CH group twisted 180<sup>o</sup>, then one H atoms is moved within the molecule somewhat, and into the attractive region of more carbon and hydrogen atoms. Also, this twist means the two 'halves' of the molecule are not not directly over each other in space - before, they were, but they were far away, so steric bumping is unlikely, but may make a slight repulsive contribution. This has however now been removed. We took the gauche-conformation, twisted a CH<sub>2</sub>CH group by 180<sup>o</sup>, and then optimised to HF/3-21G level of theory, and the resulting energy was -231.69266 Eh = -145389.46 kcalmol<sup>-1</sup>. The resulting geometry was C<sub>1</sub>-symmetric, corresponding to Gauche 3 in Appendix 1<ref name='one'>[[Mod:phys3#Appendix_1]]</ref>. This is 0.62 kcalmol<sup>-1</sup> more stable than the other Gauche conformer, by virtue of extra attractive van der Waals interactions. Also, this is 0.036 kcalmol<sup>-1</sup> more stable than the anti conformer. This is surprising, showing that the van der Waals interactions do make a significant contribution to the energy of the molecule, and in this case, overall, the energy is lower, by a small amount. However, in the Gauche conformers, we saw we have many van der Waals interactions, whereas in the anti conformer, we had few, so we can say overall, that on the anti-conformer, the σ/σ* is greater than in the gauche-conformers.

We should also be able to imagine another low-energy conformation of the anti-geometry. In Anti-1, the CH<sub>2</sub>CH groups are both twisted the same way with respect to the central anti-linkage, resulting in C<sub>2</sub> symmetry. Above, we twisted one group and found a lower energy gauche conformer. Let's do the same now. Twisting one CH<sub>2</sub>CH group and optimising to HF/3-21G resulted in a C<sub>i</sub>-symmetric geometry with energy -231.692535 Eh = -145389.38 kcalmol<sup>-1</sup>, corresponding to Anti-2 in appendix 1<ref name='one'>[[Mod:phys3#Appendix_1]]</ref>. This is 0.042 kcalmol<sup>-1</sup> higher in energy than the Anti-1 conformer. In this case, twisting of the group did not result in a lower energy conformer.

<table border='1'>
<tr>
<td colspan='5'>
'''1,5-Hexadiene Conformers /HF 3-21G'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Anti-1'''
</td>
<td>
'''Anti-2'''
</td>
<td>
'''Gauche-2'''
</td>
<td>
'''Gauche-3'''
</td>
</tr>
<tr>
<td valign='top'>
'''Geometry'''
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Anti-1</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copeanti1.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Anti-2</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copeanti2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Gauche-2</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copegauche2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>1,5-Hexadiene Gauche-3</title><color>white</color><size>150</size>
<script>rotate;</script>
<uploadedFileContents>pm08copegauche3.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td>
'''Energy /Eh'''
</td>
<td>
-231.69260
</td>
<td>
-231.69254
</td>
<td>
-231.69167
</td>
<td>
-231.69266
</td>
</tr>
<tr>
<td>
'''Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
0.036
</td>
<td>
0.078
</td>
<td>
0.62
</td>
<td>
0.0
</td>
</tr>
</table>

Let us make a comparison between different levels of theory. Above, we used HF/3-21G. Now, we are going to take our low-energy conformer, listed in the table above and re-optimise, using DFT/B3LYP/6-31G*. We shall also carry out a frequency analysis for these geometries, to verify that we have indeed reached a minimum.

<table border='1'>
<tr>
<td colspan='7'>
'''Comparison between levels of theory in the optimisation of 1,5-Hexadiene'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''HF 3-21G Energy /Eh'''
</td>
<td>
'''DFT B3LYP 6-31G* Energy /Eh'''
</td>
<td>
'''Difference /Eh'''
</td>
<td>
'''HF 3-21G Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
'''DFT B3LYP 6-31G* Relative Energy /kcalmol<sup>-1</sup>'''
</td>
<td>
'''Imaginary modes /cm<sup>-1</sup>'''
</td>
</tr>
<tr>
<td>
'''Anti-1 (C<sub>2</sub>)'''
</td>
<td>
-231.69260
</td>
<td>
-234.61180
</td>
<td>
2.91920
</td>
<td>
0.036
</td>
<td>
0.0
</td>
<td>
-8.41

-3.82
</td>
</tr>
<tr>
<td>
'''Anti-2 (C<sub>i</sub>)'''
</td>
<td>
-231.69254
</td>
<td>
-234.61172
</td>
<td>
2.91902
</td>
<td>
0.078
</td>
<td>
0.052
</td>
<td>
-6.20
</td>
</tr>
<tr>
<td>
'''Gauche-2 (C<sub>2</sub>)'''
</td>
<td>
-231.69167
</td>
<td>
-234.61069
</td>
<td>
2.91867
</td>
<td>
0.62
</td>
<td>
0.70
</td>
<td>
-13.97

-13.36

-11.10
</td>
</tr>
<tr>
<td>
'''Gauche-3 (C<sub>1</sub>)'''
</td>
<td>
-231.69266
</td>
<td>
-234.61133
</td>
<td>
2.91918
</td>
<td>
0.0
</td>
<td>
0.30
</td>
<td>
-4.40
</td>
</tr>
</table>

Between the two sets of theory, we see that the higher level DFT method has calculated a different relative energy order of our conformers. The two levels of theory do however give the same order of stabilities between the pairs of anti- and gauche- conformers, so this suggests that the DFT calculated a greater σ/σ* stabilising interaction, or a weak vdW stabilising interaction. Hence, the gauche are calculated to be less stable than the anti conformers under DFT/B3LYP/6-31G*.

There is however, a slightly worrying result when we look at the imaginary frequencies. These should all be zero, if we have indeed optimised to a minimum. I think perhaps using this mid level basis set, that the geometry hasn't quite reached the minimum. Because the energy differences are very small between conformers, a slight difference in geometry could lead us to an incorrect order of relative energies. Hence, the optimisation was rerun again, from the DFT result, this time specifying very tight convergance criteria, and int=ultrafine This is computationally expensive, but I think it is necessary to establish which is the lowest energy conformer. The results:

<table border='1'>
<tr>
<td colspan='4'>
'''DFT B3LYP 6-31G* Very tight optimisation 1,5-Hexadiene Conformers'''
</td>
</tr>
<tr>
<td>
'''Anti-1 (C<sub>2</sub>)'''
</td>
<td>
-234.61179
</td>
<td>
0.0
</td>
<td>
-6.6

-3.2
</td>
</tr>
<tr>
<td>
'''Anti-2 (C<sub>i</sub>)'''
</td>
<td>
-234.61171
</td>
<td>
0.051
</td>
<td>
-5.6

-1.9
</td>
</tr>
<tr>
<td>
'''Gauche-2 (C<sub>2</sub>)'''
</td>
<td>
-234.61070
</td>
<td>
0.68
</td>
<td>
-5.8

-5.4

-4.2
</td>
</tr>
<tr>
<td>
'''Gauche-3 (C<sub>1</sub>)'''
</td>
<td>
-234.61133
</td>
<td>
0.29
</td>
<td>
-0.0004
</td>
</tr>
</table>

This very tight convergence reduced the magnitude of all of the imaginary modes, showing the geometry is moving toward the bottom of the potential well. The key result here is that the energy changed only by ~0.01 kcalmol<sup>-1</sup>, and the order of conformers did not change. If we consider the potential surface for this molecule, we expect wells for the conformers we have found. For the two pairs of anti and gauche conformers, the geometry difference is not a great deal, to the wells are close, and probably not very deep between them. Hence, this may also explain why we get small imaginary frequencies – we are not at a transition structure, but in a shallow well, not quite at the bottom. Because this result agrees with that for the quicker calculation, we shall use the DFT B3LYP 6-31G* theory for further analysis.

[[Image:pm08anti2thermochemistry.png|right]]
The energies reported are for the conformations at 0K. Carrying out a frequency analysis allows us to make a correction to other temperatures, specified using a readisotopes keyword. Using the Anti-2 conformer, we are going to invetsigate the effect of increasing temperature on the energy of the system, taking into account the thermal correction, by calcuating the thermal corretion at a range of temperatures, by specifying a frwquency calculation to the DFT B3LYP 6-31G* level, with the readisotopes tag, on a DFT B3LYP 6-31Gd optimised geometry, and then plotting the resulting Sum of Electronic, ZPE and thermal energies.

We initially see that at low temperatures, the energy is increasing, at an increasing rate with increasing temperature, until a point where the increase in energy of the system is linear with temperature. At T=0k, all the molecules are in their vibrational ground state. As T is rasied, but kept low, the first few vibrationally excited states begin to be populated. Increasing the thermal energy further will populate more states until it gets to a point where all the vibrational states are filled. In this regime, we see an increasing reat of change of energy with tempeture. At this point, the discrete proporties of the molecules can be treated classically, i.e the vibrational temperature. After this temperature is surpassed, the molecule bahaves classically, and its increase in energy is linear with temperature.

===Locating the Transition State Structures===

[[Image:pm08copechairboatts.png|left]]
We are going to use a variety of methods to explore the transition state geometries of this rearrangement. Initially, we shall form a guess, consisting of two allyl fragments separated in space, with the correct symmetry to hopefully optimise to the transition structure. We shall use the Berny TS method to optimise, and also the 'Frozen' Coordinate, two-stage optimisation method. Then, we shall use the QST2 method, now, not forming a transition state guess, but interpolating between the starting material and product.

If we consider two allyl fragments separated in space, we can form two potential transition state structures, corresponding to chair and boat cyclohexyl-like geometries. We shall explore both reaction pathways, via chair and boat TS structures, to determine which is the lower energy, and hence more favorable process.

====Berny Optimisation====
[[Image:pm08copetsguesses.png|right]]
Using Gaussview 3.09 GUI, an allyl, C<sub>3</sub>H<sub>5</sub>, fragment was created. This was optimised using HF 3-21G theory, and the resulting geometry was then used to build our transition state guesses. Two of these fragments were placed face on, one overlapping directly, to give a C2v-symmetric geometry - Boat, and once with one fragment rotated, with a terminal C overlapping with terminal H on the other fragment, to give a C2h-symmetric geometry - Chair. The two allyl fragments were set 2.2A apart in both starting guesses.

These structures were then optimised to a Transition State, using the Berny method and HF/3-21G theory, calculating the force constants once. The resulting geometries are shown below. In both structures, the central C atom of the allyl fragments pucker away from the other fragment slightly. In the chair C2h structure, the terminal C atoms are separated by 2.02A. In the C2v boat, they are separated by 2.14A.

<table border='1'>
<tr>
<td colspan='2'>
'''HF 3-21G TS(Berny) Opt results'''
</td>
</tr>
<tr>
<td>
Chair-C2h
</td>
<td>
Boat-C2v
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Cope Chair TS Benry Optimisation result</title><color>white</color><size>150</size>
<script>rotate; measure 1 10;</script>
<uploadedFileContents>pm08copechairtsberny.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Cope Boat TS Benry Optimisation result</title><color>white</color><size>150</size>
<script>rotate; measure 1 10;</script>
<uploadedFileContents>pm08copeboattsberny.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Note that although Jmol draws these as propene fragments, the two C-C bond lengths in each fragment are equal and they are in reality allyl like. How do we know these are transition states? We look for one imaginary mode, corresponding to the displacement either side of the transition state. In the Chair-C<sub>2</sub>h TS, we find exactly that, an imaginary frequency with magnitude 817cm<sup>-1</sup>. Likewise, in the Boat-C<sub>2</sub>v TS, at -840cm-1. Animating these imaginary modes, we see each allyl fragment bend back and forth from each other. This is the Cope rearrangement.

<table border='1'>
<tr>
<td colspan='2'>
'''HF 3-21G TS(Berny) Opt Imaginary modes'''
</td>
</tr>
<tr>
<td>
'''Chair-C<sub>2</sub>h'''
</td>
<td>
'''Boat-C<sub>2</sub>v'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Cope Chair TS Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 3;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834132.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Cope Boat TS Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 3;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834131.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td>
-817cm<sup>-1</sup>
</td>
<td>
-840cm<sup>-1</sup>
</td>
</tr>
</table>

====Frozen Coordinate Optimisation====

The transition state structure guesses were taken and using the redundant coordinate tool in Gaussview, the terminal C atoms of the two fragments were frozen, at a set distance of 2.2Å apart. What this does is fix the position of these atoms when we optimise the structure. We carried out a HF/3-21G Opt=Modredundant calculation. In the resulting geometry, the central C atoms had puckered out slightly, as they did above, but as we said, the terminal atoms stayed fixed. Then we took this resulting geometry and optimised again, using the same theory, this time without the condition of being fixed, but to differentiate along the forming and breaking bonds to find the transition state. The value in this method is that we do not have to calculate force constants, which for large jobs will be less computationally expensive.

How do these compare to the Berny Results? If we measure the following geometric parameters, in both the chair and boat structures for both optimisation methods, we find them to be be identical to 0.01Å and 0.1<sup>o</sup>. Hence, we can say that for this simple system, both methods of optimising a transition state from a guess are equally valid.

<table border='1'>
<tr>
<td colspan='5'>
'''Comparing Optimised TS structures for two different methods'''
</td>
</tr>
<tr>
<td colspan='5'>
[[Image:pm08guesstscompare.png]]
</td>
</tr>
<tr>
<td rowspan='2'>
'''Parameter'''
</td>
<td colspan='2'>
'''HF 3-21G Berny TS Optimisation'''
</td>
<td colspan='2'>
'''HF 3-21G Frozen Coordinate TS Optimisation'''
</td>
</tr>
<tr>
<td>
Chair
</td>
<td>
Boat
</td>
<td>
Chair
</td>
<td>
Boat
</td>
</tr>
<tr>
<td>
a
</td>
<td>
2.02
</td>
<td>
2.14
</td>
<td>
2.02
</td>
<td>
2.14
</td>
</tr>
<tr>
<td>
b
</td>
<td>
2.88
</td>
<td>
2.78
</td>
<td>
2.88
</td>
<td>
2.78
</td>
</tr>
<tr>
<td>
c
</td>
<td>
120.5
</td>
<td>
121.7
</td>
<td>
120.5
</td>
<td>
121.7
</td>
</tr>
<tr>
<td>
d
</td>
<td>
1.39
</td>
<td>
1.38
</td>
<td>
1.39
</td>
<td>
1.38
</td>
</tr>
</table>

====QST2 and QST3====

As well as being able to set up a guess geometry of a transition state,and optimise to it using the two methods above, we can also carry out a QST2 calculation, whereby we interpolate between starting material and product, to locate the transition state along that path. This is what we shall attempt to do here, for the boat transition state

We shall take out Anti-2 C<sub>i</sub> 1,5-Hexadiene Conformer. As we saw, this is not the lowest energy conformer, but is only ca. 0.5 kcalmol<sup>-1</sup> higher in energy, so is very thermally accessible. We are going to take this conformer because, as we shall see, it has symmetry about a point, and when we set the dihedral, to come, about a plane, so the interpolation will be easier, and hence less computationally expensive and more likley to work

A necessary condition for QST2 is that the order of atoms in the reactant input metches that in the product input. Because the reactant and product are the same molecule, but a different order of atoms, our first task is to create a molgroup, with two frames of the same stutcure, then renumber the second frame accordingly, so that when the molecule rearranges via a [3,3] shift, the order is the same. Once this was done, a HF 3-21G QST2 calculation was carried out. This job however, failed and produced an erronious geometry. This is because the simple interpolation moved atoms about, but looking at the geometries, we can easily see that to be able to get to the transition sate, the C<sub>i</sub> anti structure clearly needs first to rotate about the central C-C. We then took the starting geometries from the failed QST2 job, and set the central C<sub>4</sub> dihedral to 0<sup>o</sup>. Then the two halves of the molecule were brought closer together by setting internal bond angles to both be 100<sup>o</sup>. This structure has symmetry about a plane passing across the centre of the molecule, hence, when we interpolate between the two, we should find the boat transition state, since it also has that plane-symmetry. The calculation was rerun from these starting geometries.

<table border='1'>
<tr>
<td colspan='2'>
''' Boat QST2 TS Optimisation start and end points: Failed job'''
</td>
<td rowspan='3'>
</td>
<td colspan='2'>
''' Boat QST2 TS Optimisation start and end points: Rotated Dihedral'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Start Point
</td>
<td>
End Point
</td>
</tr>
<tr>
<td>
[[Image:pm08Anti2QST2start.png|200px]]
</td>
<td>
[[Image:pm08Anti2QST2end.png|200px]]
</td>
<td>
[[Image:pm08Antirotated2QST2start.png|200px]]
</td>
<td>
[[Image:pm08Antirotated2QST2end.png|200px]]
</td>
</tr>
</table>

The result is indeed that expected - the boat transition state. Again, when we compare the resulting structural parameters to those listed above, we find them to be the same.

For more complex jobs, it is possible to specify a guess structure for the transition state - for example, here we could place in the guesses from above. This would then be a QST3 calculation. However, here it will be unnecessary, since some though as to the starting geometry emabld us to quickly find the transition state.

===Following the reaction pathway: IRC===
[[Image:pm08CopeChairIRC.png|700px|right]]

[[Image:pm08CopeBoatIRC.png|700px|right]]

[[Image:pm08Coperelativeenergy.png|700px|right]]

We have found chair and boat transition structures for the Cope rearrangement of 1,5-Hexadiene. Now we need to determine which starting conformation is necessary to reach those transition states. To do this, we use the Intrisic Reaction COOrdinat method. Here, we start at the geometry of our chosen transiton state to invensitgae, and we choose to follow the reaction path as the energy decreases down to a minimum geometry - we are following the reaction coordinate in an energy profile plot. In ths case of the Cipe rearragment, the profile will be symmetrucal about the transntion state (same molecule and conformation) but usually products have lower energy than reactants, hence, we usually follow the path in both directions but here we only have to go in one direction.

From the optimised geometry of the transition state, taken from he results of the Berny Optimisation (althogh as we saw the other methods gave the same structure), an IRC calculation was carried out, to follow the forward direction, with a maximum number of points set to 200, and specifying that the force constants be calculated at every step. Because we set the calculation to see if we have reached a minimum at every step, we don't risk not finding the true minimum.

If we observe the strctures of the final IRC geometry, we can judge which conformer the reaction proceeds from. From the Chair-TS IRC results, we find that the Gauche-2 confomation gives the necessary orientation for this rearrangement. The boat form however converges to a staggered form, which as we know is itself a transition state between lower energy gauche and/or anti conformations. This first seems to sugest the IRC failed, but if we consider that the caluclation finds the nearest minimum in the give direction, then thsi condition is fulfilled by a transition state - just the wrong type. Then, to find the nearest stable conformer, we can run another IRC on the resulting staggered geometry. Doing this, we find the calculation converges to the Gauche-3 conformer, by rotation by 60o of the central C-C bond.

These two starting conformations are, as we saw, not the lowest energy conformers. However, all the conformers, and the transition states between them were thermally accessible, i.e this system did not exhibit atropisomerism, taking an ensemble average of the system we would find a certain proportion of the molecules to be in each state, with smaller proportions for higher energy conformations.

We also see, by plotting together the energy difference between reactant and product for the two pathways, we find that the boat transition state is higher in energy than the chair transition state on the pathway between their respective conformations to allow reaction.

To be able to report a calculated activation energy for the reaction, we first need to reoptimise our transition structures to DFT B3LYP 6/31G* theory, and compare their energies to that of the Anti-1 conformer, since by convention the activation energy is reported relative to the lowest energy conformer. The activation energy between chair TS and Anti-1 Conformer is cauclated to be 34.4 kcalmol-1. The experimentally determined value is 33.5±0.5kcalmol-1. The activation energy between boat TS and Anti-1 Conformer is calculated to be 43.1 kcalmol-1. The experimentally determined value is 44.7±0.2 kcalmol-1. These are at 0K, so I assume the experimental values are extrapolations of higher T data, hence the error. We find our two values to be very close to those predicted,

</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79364

2010-12-17T11:47:03Z

Pm08: /* Transition States */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane]]
In Module 1, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we rationalised as being due to a more favorable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall re-investigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, when looking through literature whilst studying that reaction, I found a paper, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl<sub>3</sub>. AlCl<sub>3</sub> acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-structure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as "''(having) no direct precedent and is therefore subject to some suspicion. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.''" This step will be examined, by modeling the reactant and product and looking for the transition state and reaction path, to determine its feasibility.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo- forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and carbon tetrahedral fragments, adjusting bond lengths, types and angles accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol<sup>-1</sup> more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Cyclopentadiene
</td>
<td>
-194.101058
</td>
<td>
-121800.3549
</td>
</tr>
<tr>
<td>
Endo-DCPD
</td>
<td>
-388.2280216
</td>
<td>
-243616.9658
</td>
</tr>
<tr>
<td>
Exo-DCPD
</td>
<td>
-388.2297763
</td>
<td>
-243618.0669
</td>
</tr>
</table>

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo- form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to to be the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, seperated in space, in the correct relative orientations to each other, and the corresponding product diastereoisomer, with the atomic labeling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels Alder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. The vibrational modes of the transition states were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm<sup>-1</sup>, and in the exo-isomer, had magnitude 719cm<sup>-1</sup>. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo-DCPD TS
</td>
<td>
-388.1711242
</td>
<td>
-243581.2621
</td>
</tr>
<tr>
<td>
Exo-DCPD TS
</td>
<td>
-388.1667293
</td>
<td>
-243578.5043
</td>
</tr>
</table>

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new sigma bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways together, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picture we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favorable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol<sup>-1</sup>, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better reprensented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

Wit the complex molecular geometry in the product and reactant, forming a guess transiton state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transiton state as having its charge again delicalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. to HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise intiially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

The calculated activation energy on going from intermediate XX to TS is 26.44 kcalmol-1. The reaction from XX to XXI is very slightly endothermic with a reaction enthalpy of +0.77 kcalmol-1.

If this process possible? The authors proposed the pathway based upon analysis of the strain of the system - the highly strained endo-tetrahydrodicyclopentadiene rearranging to release strain. However, as we can see from the energies, there is no releif of strain, and the associated gain in stability, because the energy of the starting material and product are very similar, in fact the enrgy of the product as defined here is slightly higher in energy! This s because the two systems are both equaly strained- by delocalisoing the charge, the systems are able to reduce some strain already, so the molecule is not confomed to the bicyclic geometry, which the authors predicted above. So thermodynamically, there is no desire for this process to occur. But the energy difference is minimal between the two carbocations, so we would expect an equlibrium to exost between the twi. The transition state energy is not too high so as to not be obtainable, expectally considering we are heating the mixture. hence, we can say this process may be occuring, to set up an equlibrium between the two, but there is no great preference for either system. If the reaction from XXI is fast, this could be removed from equlibrium and we would slowly see XX disappear, as XXI is converted. Hence, this step could be involved.

<table border='1'>
<tr>
<td colspan='3'>
'''Rearrangement Species Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Intermediate:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Intermediate XX
</td>
<td>
-389.7989889
</td>
<td>
-244602.7635
</td>
</tr>
<tr>
<td>
Transition State
</td>
<td>
-389.7568615
</td>
<td>
-244576.3281
</td>
</tr>
<tr>
<td>
Intermediate XXI
</td>
<td>
-389.8002186
</td>
<td>
-244603.5352
</td>
</tr>
</table>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79364

2010-12-17T11:45:33Z

Pm08: /* Reactants and Products */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane]]
In Module 1, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we rationalised as being due to a more favorable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall re-investigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, when looking through literature whilst studying that reaction, I found a paper, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl<sub>3</sub>. AlCl<sub>3</sub> acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-structure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as "''(having) no direct precedent and is therefore subject to some suspicion. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.''" This step will be examined, by modeling the reactant and product and looking for the transition state and reaction path, to determine its feasibility.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo- forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and carbon tetrahedral fragments, adjusting bond lengths, types and angles accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol<sup>-1</sup> more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Cyclopentadiene
</td>
<td>
-194.101058
</td>
<td>
-121800.3549
</td>
</tr>
<tr>
<td>
Endo-DCPD
</td>
<td>
-388.2280216
</td>
<td>
-243616.9658
</td>
</tr>
<tr>
<td>
Exo-DCPD
</td>
<td>
-388.2297763
</td>
<td>
-243618.0669
</td>
</tr>
</table>

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo- form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to to be the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, seperated in space, in the correct relative orientations to each other, and the corresponding product diastereoisomer, with the atomic labeling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels Alder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. The vibrational modes of the transition states were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm<sup>-1</sup>, and in the exo-isomer, had magnitude 719cm<sup>-1</sup>. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction.

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new sigma bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways together, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picture we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favorable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol<sup>-1</sup>, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better reprensented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

Wit the complex molecular geometry in the product and reactant, forming a guess transiton state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transiton state as having its charge again delicalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. to HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise intiially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

The calculated activation energy on going from intermediate XX to TS is 26.44 kcalmol-1. The reaction from XX to XXI is very slightly endothermic with a reaction enthalpy of +0.77 kcalmol-1.

If this process possible? The authors proposed the pathway based upon analysis of the strain of the system - the highly strained endo-tetrahydrodicyclopentadiene rearranging to release strain. However, as we can see from the energies, there is no releif of strain, and the associated gain in stability, because the energy of the starting material and product are very similar, in fact the enrgy of the product as defined here is slightly higher in energy! This s because the two systems are both equaly strained- by delocalisoing the charge, the systems are able to reduce some strain already, so the molecule is not confomed to the bicyclic geometry, which the authors predicted above. So thermodynamically, there is no desire for this process to occur. But the energy difference is minimal between the two carbocations, so we would expect an equlibrium to exost between the twi. The transition state energy is not too high so as to not be obtainable, expectally considering we are heating the mixture. hence, we can say this process may be occuring, to set up an equlibrium between the two, but there is no great preference for either system. If the reaction from XXI is fast, this could be removed from equlibrium and we would slowly see XX disappear, as XXI is converted. Hence, this step could be involved.

<table border='1'>
<tr>
<td colspan='3'>
'''Rearrangement Species Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Intermediate:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Intermediate XX
</td>
<td>
-389.7989889
</td>
<td>
-244602.7635
</td>
</tr>
<tr>
<td>
Transition State
</td>
<td>
-389.7568615
</td>
<td>
-244576.3281
</td>
</tr>
<tr>
<td>
Intermediate XXI
</td>
<td>
-389.8002186
</td>
<td>
-244603.5352
</td>
</tr>
</table>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79364

2010-12-17T11:44:53Z

Pm08: /* Reactants and Products */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane]]
In Module 1, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we rationalised as being due to a more favorable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall re-investigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, when looking through literature whilst studying that reaction, I found a paper, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl<sub>3</sub>. AlCl<sub>3</sub> acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-structure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as "''(having) no direct precedent and is therefore subject to some suspicion. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.''" This step will be examined, by modeling the reactant and product and looking for the transition state and reaction path, to determine its feasibility.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo- forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and carbon tetrahedral fragments, adjusting bond lengths, types and angles accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol<sup>-1</sup> more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

<table border='1'>
<tr>
<td>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Cyclopentadiene
</td>
<td>
-194.101058
</td>
<td>
-121800.3549
</td>
</tr>
<tr>
<td>
Endo-DCPD
</td>
<td>
-388.2280216
</td>
<td>
-243616.9658
</td>
</tr>
<tr>
<td>
Exo-DCPD
</td>
<td>
-388.2297763
</td>
<td>
-243618.0669
</td>
</tr>
</table>

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo- form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to to be the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, seperated in space, in the correct relative orientations to each other, and the corresponding product diastereoisomer, with the atomic labeling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels Alder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. The vibrational modes of the transition states were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm<sup>-1</sup>, and in the exo-isomer, had magnitude 719cm<sup>-1</sup>. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction.

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new sigma bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways together, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picture we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favorable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol<sup>-1</sup>, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better reprensented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

Wit the complex molecular geometry in the product and reactant, forming a guess transiton state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transiton state as having its charge again delicalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. to HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise intiially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

The calculated activation energy on going from intermediate XX to TS is 26.44 kcalmol-1. The reaction from XX to XXI is very slightly endothermic with a reaction enthalpy of +0.77 kcalmol-1.

If this process possible? The authors proposed the pathway based upon analysis of the strain of the system - the highly strained endo-tetrahydrodicyclopentadiene rearranging to release strain. However, as we can see from the energies, there is no releif of strain, and the associated gain in stability, because the energy of the starting material and product are very similar, in fact the enrgy of the product as defined here is slightly higher in energy! This s because the two systems are both equaly strained- by delocalisoing the charge, the systems are able to reduce some strain already, so the molecule is not confomed to the bicyclic geometry, which the authors predicted above. So thermodynamically, there is no desire for this process to occur. But the energy difference is minimal between the two carbocations, so we would expect an equlibrium to exost between the twi. The transition state energy is not too high so as to not be obtainable, expectally considering we are heating the mixture. hence, we can say this process may be occuring, to set up an equlibrium between the two, but there is no great preference for either system. If the reaction from XXI is fast, this could be removed from equlibrium and we would slowly see XX disappear, as XXI is converted. Hence, this step could be involved.

<table border='1'>
<tr>
<td colspan='3'>
'''Rearrangement Species Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Intermediate:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Intermediate XX
</td>
<td>
-389.7989889
</td>
<td>
-244602.7635
</td>
</tr>
<tr>
<td>
Transition State
</td>
<td>
-389.7568615
</td>
<td>
-244576.3281
</td>
</tr>
<tr>
<td>
Intermediate XXI
</td>
<td>
-389.8002186
</td>
<td>
-244603.5352
</td>
</tr>
</table>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79364

2010-12-17T11:37:17Z

Pm08: /* The Pathway to Adamantane */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane]]
In Module 1, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we rationalised as being due to a more favorable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall re-investigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, when looking through literature whilst studying that reaction, I found a paper, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl<sub>3</sub>. AlCl<sub>3</sub> acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-structure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as "''(having) no direct precedent and is therefore subject to some suspicion. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.''" This step will be examined, by modeling the reactant and product and looking for the transition state and reaction path, to determine its feasibility.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo- forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and carbon tetrahedral fragments, adjusting bond lengths, types and angles accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol<sup>-1</sup> more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo- form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to to be the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, seperated in space, in the correct relative orientations to each other, and the corresponding product diastereoisomer, with the atomic labeling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels Alder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. The vibrational modes of the transition states were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm<sup>-1</sup>, and in the exo-isomer, had magnitude 719cm<sup>-1</sup>. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction.

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new sigma bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways together, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picture we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favorable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol<sup>-1</sup>, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better reprensented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

Wit the complex molecular geometry in the product and reactant, forming a guess transiton state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transiton state as having its charge again delicalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. to HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise intiially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

The calculated activation energy on going from intermediate XX to TS is 26.44 kcalmol-1. The reaction from XX to XXI is very slightly endothermic with a reaction enthalpy of +0.77 kcalmol-1.

If this process possible? The authors proposed the pathway based upon analysis of the strain of the system - the highly strained endo-tetrahydrodicyclopentadiene rearranging to release strain. However, as we can see from the energies, there is no releif of strain, and the associated gain in stability, because the energy of the starting material and product are very similar, in fact the enrgy of the product as defined here is slightly higher in energy! This s because the two systems are both equaly strained- by delocalisoing the charge, the systems are able to reduce some strain already, so the molecule is not confomed to the bicyclic geometry, which the authors predicted above. So thermodynamically, there is no desire for this process to occur. But the energy difference is minimal between the two carbocations, so we would expect an equlibrium to exost between the twi. The transition state energy is not too high so as to not be obtainable, expectally considering we are heating the mixture. hence, we can say this process may be occuring, to set up an equlibrium between the two, but there is no great preference for either system. If the reaction from XXI is fast, this could be removed from equlibrium and we would slowly see XX disappear, as XXI is converted. Hence, this step could be involved.

<table border='1'>
<tr>
<td colspan='3'>
'''Rearrangement Species Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Intermediate:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Intermediate XX
</td>
<td>
-389.7989889
</td>
<td>
-244602.7635
</td>
</tr>
<tr>
<td>
Transition State
</td>
<td>
-389.7568615
</td>
<td>
-244576.3281
</td>
</tr>
<tr>
<td>
Intermediate XXI
</td>
<td>
-389.8002186
</td>
<td>
-244603.5352
</td>
</tr>
</table>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T11:30:20Z

Pm08: /* The Diels Alder Cycloaddition between Butadiene and Ethene */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]
The Diels Alder reaction is a pi4s + pi2s cycloaddition between a diene and a dienophile, to form two new sigma bonds from the termini of a conjugated pi system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry propoerties of the Frontier orbitals of the reactants, we will show that this reactio is allowed, and make a prediciton as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transiiton state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloaditon between Maleic anhydride acting ad the dienophile and 1,3Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reactning. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations. Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal pi system, featuring a pi homo and pi* LUMO. The HOMO is symmetirc with respect to a plane bisecting the molesule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a pi system, with equal coefficients on both pi orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the pi* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new sigma bonds, if one is empty and one is filled. Becuase of the symmetry constraint, the geomerty of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from pi bonds, we have to rehybrise sp2 to sp3, and we require the pi bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combinations of FOs , above. We couldn't make a guess as to which case we have without calculaiton, because these are both fairly 'electronically neutral' alkenes, i.e no electron puching or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene pi bond forming, and the ethene pi bond and cis-butadiene pi bonds breaking, with increasing electron desity inbetween the two moelcules, where the sigma bonds are forming.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinsaions.

==Optimising reactants and product==

Compared to the Cope rearranegent, the Diels Alder reaction is Bimolecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32A.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minim and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5o intervals, ie a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomolous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90o, and a maximum in the energy profile, 7.56 kcalmol-1 higher in energy than the trans conformer. At 90o apart, the pi systems are orthogonal, so there can be no conjugation whatsoever. At 0o, the two pi systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130o, which is 3.54 Kcalmol-1 higher in energy than the trans conformer. In this case, we have a balence of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stornger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is infact a transition state, not a stable conformer, and is 3.88 kcalmol-1 higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130o-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90o-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyckohexane conformation, we can make some educated guesses as to what will be the stable minima , then we shall test our predictions by optimising to try to find these strutcures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposd by the doubel bind, we can imagine two mimima conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A hlaf oat structure was created by taking a bicyclo system, and removing one CH2CH2 group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol-1.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels ALder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST 2 calcualtion interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labelling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the pi system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to reoptimiseour HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol-1. The calculated free eneergy change of reaction is -43.1 kcalmol-1.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79364

2010-12-17T11:28:03Z

Pm08: /* Following the reaction Path */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane]]
In Module 1, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we reationalised as being due to a more favourable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall reinvesigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, whilst looking through literature whilst studying that reaction, I found a paper, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl3. ALCl3 acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-strutcure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as ''(having) no direct precedent and is therefore subject to some suspision. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.'' This step will be examined, by modelling the reactant and product and looking for the transition state and reaction path.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and arobon tetrehedral fragments, adjusting bond lengths, types and alges accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol-1 more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to tbe the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, seperated in space, in the correct relative orientations to each other, and the corresponding product diasteriisomer, with the atomic labelling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels ALder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. To the HF 3/21G level of theory. The vibrational modes of the transition staes were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm-1, and in the exo-isomer, had magnitude 719cm-1. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new sigma bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways togther, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the Endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picure we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favourable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, by reoptimising to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better reprensented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

Wit the complex molecular geometry in the product and reactant, forming a guess transiton state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transiton state as having its charge again delicalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. to HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise intiially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

The calculated activation energy on going from intermediate XX to TS is 26.44 kcalmol-1. The reaction from XX to XXI is very slightly endothermic with a reaction enthalpy of +0.77 kcalmol-1.

If this process possible? The authors proposed the pathway based upon analysis of the strain of the system - the highly strained endo-tetrahydrodicyclopentadiene rearranging to release strain. However, as we can see from the energies, there is no releif of strain, and the associated gain in stability, because the energy of the starting material and product are very similar, in fact the enrgy of the product as defined here is slightly higher in energy! This s because the two systems are both equaly strained- by delocalisoing the charge, the systems are able to reduce some strain already, so the molecule is not confomed to the bicyclic geometry, which the authors predicted above. So thermodynamically, there is no desire for this process to occur. But the energy difference is minimal between the two carbocations, so we would expect an equlibrium to exost between the twi. The transition state energy is not too high so as to not be obtainable, expectally considering we are heating the mixture. hence, we can say this process may be occuring, to set up an equlibrium between the two, but there is no great preference for either system. If the reaction from XXI is fast, this could be removed from equlibrium and we would slowly see XX disappear, as XXI is converted. Hence, this step could be involved.

<table border='1'>
<tr>
<td colspan='3'>
'''Rearrangement Species Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Intermediate:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Intermediate XX
</td>
<td>
-389.7989889
</td>
<td>
-244602.7635
</td>
</tr>
<tr>
<td>
Transition State
</td>
<td>
-389.7568615
</td>
<td>
-244576.3281
</td>
</tr>
<tr>
<td>
Intermediate XXI
</td>
<td>
-389.8002186
</td>
<td>
-244603.5352
</td>
</tr>
</table>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79365

2010-12-17T11:18:55Z

Pm08:

=Adamantane Rearrangement IRC=

This movie shows the path from intermediate XXI to XX, that is, playing in reverse.

<table border='1'>
<tr>
<td>
'''2,6-Alkyl Shift IRC Path'''
</td>
</tr>
<tr>
<td>
[[Image:pm08AdamantaneIRC.gif]]
</td>
</tr>
</table>

----

[[Mod:atbxz79364#Following_the_reaction_Path|Return]]

Rep:Mod:atbxz79364

2010-12-17T11:18:31Z

Pm08: /* Following the reaction Path */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane]]
In Module 1, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we reationalised as being due to a more favourable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall reinvesigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, whilst looking through literature whilst studying that reaction, I found a paper, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl3. ALCl3 acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-strutcure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as ''(having) no direct precedent and is therefore subject to some suspision. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.'' This step will be examined, by modelling the reactant and product and looking for the transition state and reaction path.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and arobon tetrehedral fragments, adjusting bond lengths, types and alges accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol-1 more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to tbe the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, seperated in space, in the correct relative orientations to each other, and the corresponding product diasteriisomer, with the atomic labelling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels ALder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. To the HF 3/21G level of theory. The vibrational modes of the transition staes were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm-1, and in the exo-isomer, had magnitude 719cm-1. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new sigma bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways togther, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the Endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picure we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favourable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, by reoptimising to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better reprensented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

Wit the complex molecular geometry in the product and reactant, forming a guess transiton state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transiton state as having its charge again delicalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. to HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise intiially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

If this process possible?

<table border='1'>
<tr>
<td colspan='3'>
'''Rearrangement Species Energies /DFT B3LYP 6-31G*''
</td>
</tr>
<tr>
<td>
'''Intermediate:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Intermediate XX
</td>
<td>
-389.7989889
</td>
<td>
-244602.7635
</td>
</tr>
<tr>
<td>
Transition State
</td>
<td>
-389.7568615
</td>
<td>
-244576.3281
</td>
</tr>
<tr>
<td>
Intermediate XXI
</td>
<td>
-389.8002186
</td>
<td>
-244603.5352
</td>
</tr>
</table>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79364

2010-12-17T11:14:54Z

Pm08: /* Finding the Transition state */

=The Pathway to Adamantane=
[[Image:Pm08Adamantanerearrangement.png|frame|The proposed pathway for the rearrangement of endo-tetrahydrodicyclopentadiene to give adamantane]]
In Module 1, we looked at the dimerisation of Cyclopentadiene, via a Diels Alder Cycloaddition to give endo-dicyclopentadiene only (at room temperature), which we reationalised as being due to a more favourable transition state for this diastereoisomer, due to secondary orbital overlap from the other alkene bond. We shall reinvesigate this reaction here, using the methods we have learnt, and compare to the qualitative picture we formed earlier.

Also, whilst looking through literature whilst studying that reaction, I found a paper, presenting a synthesis of the diamonoid adamantane, by rearrangement of endo-tetrahydrodicyclopentadiene in the presence of AlCl3. ALCl3 acts as a carbocation generator, which is proposed to initiate the reaction. Then, through a series of intermediates, the endo-strutcure rearranges to give adamantane. The authors proposed a rearrangement pathway.

Whilst there is not sufficient time to fully investigate this proposed pathway, there is one key step, from intermediate XX to XXI, a 2,6-alkyl migration, which the authors describe as ''(having) no direct precedent and is therefore subject to some suspision. Analogous 2,6-hydride shifts are well documented however, and a 2,6-methyl migration has been observed in a carbenoid reaction. The postulated alkyl migration in the adamantane rearrangement therefore is not altogether unreasonable.'' This step will be examined, by modelling the reactant and product and looking for the transition state and reaction path.

==The Dimerisation of Cyclopentadiene==
===Reactants and Products===

[[Image:pm08cyclopentadiene.png|left]]
First, as always, we need to optimise the reactants and products. Cyclopentadiene was created using a Gaussview fragment, and optimised initially to HF 3-21G, then using that result, to DFT B3LPY 6-31G*. Because the molecule is a diene, it is necessarily planar, so we don't have to search for other conformations.

[[Image:pm08DCPD.png|left]]
The symmetry allowed products of this cycloaddition are endo- and exo-dicyclopentadiene, though as we have said, only the endo forms at room temperature. These products were created using Gaussview, and various bicyclic fragments, and arobon tetrehedral fragments, adjusting bond lengths, types and alges accordingly. These guess structures were then optimised to HF 3-21G then DFT B3LYP 6-31G* theory. Again, these molecules are conformationally locked, so we are not concerned with other minima.

We find the exo-dimer to be 1.10 kcalmol-1 more stable than the endo-dimer. This agrees with our MM2 conclusion, which we argued was due to the steric bumping across the molecule in the endo-form, as it folded back on itself. In the exo form, the two rings are removed from each other, so this bumping is removed.

===Transition States===

Because the higher-energy endo form is the only product we can say that this is a kinetically driven process. This means that the transition state to the endo form is of lower energy than that to the exo form. We use our newly learnt techniques to show this to tbe the case.

To find the transition states, the QST2 method was used, starting from two cyclopentadiene molecules, seperated in space, in the correct relative orientations to each other, and the corresponding product diasteriisomer, with the atomic labelling changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Dicyclopentadiene Cycloaddition QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08ExoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08ExoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08ExoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08EndoDCPDQST2start.png|200px]]
</td>
<td>
[[Image:pm08EndoDCPDQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>200</size>
<script>measure 1 12; measure 2 21; rotate;</script>
<uploadedFileContents>pm08EndoDCPDTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

The interpolation between the two sets of atomic positions and then subsequent transition state optimisation carried out by QST2 resulted in the structures shown below. As was the case for the two previous Diels ALder reactions studied, we cleaned up the transition state in Gaussview, removing the false connections shown in the interface. To the HF 3/21G level of theory. The vibrational modes of the transition staes were calculated, and in each isomer, one imaginary frequency was found. In the endo-isomer this had magnitude 652cm-1, and in the exo-isomer, had magnitude 719cm-1. Animating these modes once more shows us the displacement characteristic of the Diels Alder reaction

===IRC: Reaction Pathway===

[[Image:Pm08DCPDendoIRC.png|700px|right]]

[[Image:Pm08DCPDexoIRC.png|700px|right]]

From the results of the QST2 TS optimisation, an IRC calculation was set up on each of the isomeric transition states, specifying iteration in both directions. To HF 3-21G theory. The resulting energy profiles and geometries at key points are shown below.

As the reactants approach each other, their energy rises, as steric and electronic repulsions begin to increase. As the reactants begin to change their conformations to approach the transition state, the energy rises at a steeper rate. As the new sigma bonds form, the energy quickly drops, and a negative reaction enthalpy results. Both pathways have late-transition states.

By plotting the absolute energy against the reaction coordinate for both pathways togther, we see two things. One, that the exo product is slightly lower in energy than the endo product. Two, that the Endo transition state is lower in energy than the exo transition state. This is in agreement with the qualitative picure we formed back in Module 1; that the endo kinetic product forms because its energy of activation is lower than the exo form, which we put down to favourable, transition state stabilising secondary orbital overlap, as we saw for the case of Maleic Anhydride above. There, a pi system from the carbonyl function stabilised the transition state. Here, is it the pi system from the other double bond of the cyclopentadene dienophile.

Finally, we report the activation and free energy changes for reaction, by reoptimising to DFT B3LYP 6-31g* theory. The Endo Pathway activation energy is calculated at 19.45 kcalmol, wheras the exo-pathway actvation energy is calculated at 22.21 kcalmol<sup>-1</sup>. The endo enthalpy change on reaction is -35.70 kcalmol<sup>-1</sup>, and that for the exo is -39.56 kcalmol<sup>-1</sup>.

[[Image:Pm08DCPDpathways.png|700px]]

==A 2,6-Alkyl Shift?==

===Optimising XX: The endo-tetrahydrodicyclopentadiene cation===

[[Image:pm08adamantaneintXX.png|left]]
[[Image:pm08AdamantaneXXopt.png|700px|right]]
From the resulting geometry of the endo-dicyclopentadiene calculation, the two double bonds were redefined as single bonds and the lengths changed, and the valency of the carbon atoms changed accordingly. Then, one hydrogen atom was removed, and the charge of the system increased to +1 in the input file. Then, an optimisation was carried out to DFT B3LYP 6-31G* theory.

If we follow the optimisation procedure, we find that, initially, the apex with only one H atoms initially becomes planar, as expected, since this, classically, the structure of a carbocation, but then we find the system is able to further lower its energy, by delocalising that charge over three carbon centres, by dissociation of a single bond. This is an example then, of a non-classical cation. If we look at the vibrational modes, we find no imaginary frequencies, confirming that this is a minimum and not a transition state.

[[Image:pm08adamantaneintXXdelocalised.png|right]]
The jmol above shows the region of delocalisation of the charge, by looking at the valence and structure of the corresponding C atoms. Hence, the graphic above, from the paper, would be better reprensented as that shown to the right:

<table border='1'>
<tr>
<td>
'''Intermediate XX Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 4 5; measure 3 5; rotate;</script>
<uploadedFileContents>pm08AdamantaneXX.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Optimising XXI===

[[Image:pm08adamantaneintXXI.png|left]]
To find the minimum in the XXI intermediate, first, a neutral molecule was created and optimised to HF 3-21G, the using the result of this, a hydrogen was abstracted from the correct position as before, to give a structure looking much like that to the left, and reoptimised. A plot of the optimisation path is shown below.

[[Image:pm08AdamantaneXXIopt.png|right|700px]]
Again, initially, the molecule becomes planar at the low-valency apex, before again delocalising to give a non-classical cation, spread over three vertices. The representation given by the authors is poor, as it shows localised character of the cation. This as we have found is not a stable conformer, but lowers its energy further by spreading the charge. The structure is better represented as that shown:

[[Image:pm08adamantaneintXXIdelocalised.png]]

<table border='1'>
<tr>
<td>
'''Intermediate XXI Structure'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 1 2; measure 1 11; rotate;</script>
<uploadedFileContents>pm08AdamantaneXXI.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Finding the Transition state===

Wit the complex molecular geometry in the product and reactant, forming a guess transiton state would be difficult. However, this looks like a good job for QST2: most of the molecule is fixed, and in the reactant and product the same non-classical cation is seen, on opposite faces of the molecule. Hence, an interpolation between these is a good start to look for our transition state. This was carried out, numbering the reactant and product accordingly, to DFT B3LYP 3-21G Theory.

The resulting geometry predicted for the transition state shows the terminal C atoms of the alkyl chain to migrate mid way between the vertex it left and that which it is going to. Looking at the vibrationa, we find one imaginary mode at a magnitude of 387cm<sup>-1</sup>, which if we animate shows the displacement back and forth of the terminal C atoms of the alkyl chain. This suggests we have found to correct transition state for this alkyl migration.

We can graphically represent this transiton state as having its charge again delicalised over three centres, with the alkyl termini mid point passing over the front face of the system. To confirm that this transition state is that for this rearrangement process, we will conduct an IRC calculation.

[[Image:pm08adamantaneTS.png]]

<table border='1'>
<tr>
<td>
'''Adamantane Rearrangment XX to XXI TS'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Adamantane QST2</title><color>white</color><size>250</size>
<script>measure 3 10; measure 3 5; measure 5 10; rotate;</script>
<uploadedFileContents>pm08AdamantaneQST2.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

===Following the reaction Path===
[[Image:pm08AdamantaneIRC.png|right|700px]]
An IRC calculation was carried out on the transition state geometry, specifying iteration in both directions. The resulting energy profile was plotted, show below with geometries at key points. to HF 3-21G theory.

[[Mod:atbxz79365|Click here to see the IRC path...]]

We see the energy quickly rise as the geometry changes to allow the alkyl group to migrate. Previously, we tended to see a slow energy rise intiially, when we considered bimolecular reactions, as the reactants moved toward each other. However, this is unimolecuular, so the need to adjust the structure means a steep energy rise. The energy reaches a maximum as the alkyl group migrates mid way between the system. This is because the delocalised charged three centre system has been distorted heavily and 'stretched' if you like. Then, as the non-classical cation reforms the other side, the energy drops.

If this process possible?

----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T11:11:46Z

Pm08: /* Optimising Transition States */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]

The Diels Alder reaction is a pi4s + pi2s cycloaddition between a diene and a dienophile, to form two new sigma bonds from the termini of a conjugated pi system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry propoerties of the Frontier orbitals of the reactants, we will show that this reactio is allowed, and make a prediciton as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transiiton state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloaditon between Maleic anhydride acting ad the dienophile and 1,3Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reactning. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations. Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal pi system, featuring a pi homo and pi* LUMO. The HOMO is symmetirc with respect to a plane bisecting the molesule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a pi system, with equal coefficients on both pi orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the pi* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new sigma bonds, if one is empty and one is filled. Becuase of the symmetry constraint, the geomerty of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from pi bonds, we have to rehybrise sp2 to sp3, and we require the pi bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combinations of FOs , above. We couldn't make a guess as to which case we have without calculaiton, because these are both fairly 'electronically neutral' alkenes, i.e no electron puching or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene pi bond forming, and the ethene pi bond and cis-butadiene pi bonds breaking, with increasing electron desity inbetween the two moelcules, where the sigma bonds are forming.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinsaions.

==Optimising reactants and product==

Compared to the Cope rearranegent, the Diels Alder reaction is Bimolecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32A.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minim and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5o intervals, ie a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomolous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90o, and a maximum in the energy profile, 7.56 kcalmol-1 higher in energy than the trans conformer. At 90o apart, the pi systems are orthogonal, so there can be no conjugation whatsoever. At 0o, the two pi systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130o, which is 3.54 Kcalmol-1 higher in energy than the trans conformer. In this case, we have a balence of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stornger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is infact a transition state, not a stable conformer, and is 3.88 kcalmol-1 higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130o-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90o-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyckohexane conformation, we can make some educated guesses as to what will be the stable minima , then we shall test our predictions by optimising to try to find these strutcures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposd by the doubel bind, we can imagine two mimima conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A hlaf oat structure was created by taking a bicyclo system, and removing one CH2CH2 group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol-1.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels ALder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST 2 calcualtion interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labelling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the pi system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to reoptimiseour HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol-1. The calculated free eneergy change of reaction is -43.1 kcalmol-1.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T11:11:22Z

Pm08: /* Optimising Transition States */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]

The Diels Alder reaction is a pi4s + pi2s cycloaddition between a diene and a dienophile, to form two new sigma bonds from the termini of a conjugated pi system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry propoerties of the Frontier orbitals of the reactants, we will show that this reactio is allowed, and make a prediciton as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transiiton state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloaditon between Maleic anhydride acting ad the dienophile and 1,3Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reactning. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations. Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal pi system, featuring a pi homo and pi* LUMO. The HOMO is symmetirc with respect to a plane bisecting the molesule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a pi system, with equal coefficients on both pi orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the pi* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new sigma bonds, if one is empty and one is filled. Becuase of the symmetry constraint, the geomerty of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from pi bonds, we have to rehybrise sp2 to sp3, and we require the pi bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combinations of FOs , above. We couldn't make a guess as to which case we have without calculaiton, because these are both fairly 'electronically neutral' alkenes, i.e no electron puching or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene pi bond forming, and the ethene pi bond and cis-butadiene pi bonds breaking, with increasing electron desity inbetween the two moelcules, where the sigma bonds are forming.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinsaions.

==Optimising reactants and product==

Compared to the Cope rearranegent, the Diels Alder reaction is Bimolecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32A.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minim and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5o intervals, ie a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomolous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90o, and a maximum in the energy profile, 7.56 kcalmol-1 higher in energy than the trans conformer. At 90o apart, the pi systems are orthogonal, so there can be no conjugation whatsoever. At 0o, the two pi systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130o, which is 3.54 Kcalmol-1 higher in energy than the trans conformer. In this case, we have a balence of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stornger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is infact a transition state, not a stable conformer, and is 3.88 kcalmol-1 higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130o-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90o-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyckohexane conformation, we can make some educated guesses as to what will be the stable minima , then we shall test our predictions by optimising to try to find these strutcures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposd by the doubel bind, we can imagine two mimima conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A hlaf oat structure was created by taking a bicyclo system, and removing one CH2CH2 group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol-1.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels ALder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST 2 calcualtion interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labelling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the pi system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to reoptimiseour HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol-1. The calculated free eneergy change of reaction is -43.1 kcalmol-1.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Once again, we see the dienophile approach from above the plane of the ring, a requirement for an allowed reaction to preserve the symmetry with respect to the plane. The exo-TS is 2.56 kcalmol-1 higher in energy than the endo-TS, which, as we saw in our discussion above, is due to a favourable, stabilising secondary orbital overlap between the laleic anhydride carobnyl pi system, and the forming doubel bond, in this transition state.

<table border='1'>
<tr>
<td colspan='3'>
'''Transition State Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Transiton State:'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Endo:
</td>
<td>
-612.6833966
</td>
<td>
-384464.9582
</td>
</tr>
<tr>
<td>
Exo:
</td>
<td>
-612.6793109
</td>
<td>
-384462.3944
</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T11:04:56Z

Pm08: /* Optimising Reactants and Products */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]

The Diels Alder reaction is a pi4s + pi2s cycloaddition between a diene and a dienophile, to form two new sigma bonds from the termini of a conjugated pi system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry propoerties of the Frontier orbitals of the reactants, we will show that this reactio is allowed, and make a prediciton as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transiiton state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloaditon between Maleic anhydride acting ad the dienophile and 1,3Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reactning. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations. Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal pi system, featuring a pi homo and pi* LUMO. The HOMO is symmetirc with respect to a plane bisecting the molesule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a pi system, with equal coefficients on both pi orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the pi* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new sigma bonds, if one is empty and one is filled. Becuase of the symmetry constraint, the geomerty of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from pi bonds, we have to rehybrise sp2 to sp3, and we require the pi bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combinations of FOs , above. We couldn't make a guess as to which case we have without calculaiton, because these are both fairly 'electronically neutral' alkenes, i.e no electron puching or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene pi bond forming, and the ethene pi bond and cis-butadiene pi bonds breaking, with increasing electron desity inbetween the two moelcules, where the sigma bonds are forming.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinsaions.

==Optimising reactants and product==

Compared to the Cope rearranegent, the Diels Alder reaction is Bimolecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32A.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minim and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5o intervals, ie a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomolous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90o, and a maximum in the energy profile, 7.56 kcalmol-1 higher in energy than the trans conformer. At 90o apart, the pi systems are orthogonal, so there can be no conjugation whatsoever. At 0o, the two pi systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130o, which is 3.54 Kcalmol-1 higher in energy than the trans conformer. In this case, we have a balence of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stornger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is infact a transition state, not a stable conformer, and is 3.88 kcalmol-1 higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130o-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90o-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyckohexane conformation, we can make some educated guesses as to what will be the stable minima , then we shall test our predictions by optimising to try to find these strutcures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposd by the doubel bind, we can imagine two mimima conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A hlaf oat structure was created by taking a bicyclo system, and removing one CH2CH2 group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol-1.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels ALder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST 2 calcualtion interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labelling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the pi system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to reoptimiseour HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol-1. The calculated free eneergy change of reaction is -43.1 kcalmol-1.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>

</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----

Rep:Mod:atbxz79363

2010-12-17T11:04:01Z

Pm08: /* Product */

=The Diels Alder Cycloaddition between Butadiene and Ethene=
<div align='justify'>
[[Image:pm08prototypeDA.png|frame|The Diels Alder Cycloaddition between butadiene and ethene]]

The Diels Alder reaction is a pi4s + pi2s cycloaddition between a diene and a dienophile, to form two new sigma bonds from the termini of a conjugated pi system.

We shall initially investigate the prototype reaction, that between butadiene and ethene. Using the symmetry propoerties of the Frontier orbitals of the reactants, we will show that this reactio is allowed, and make a prediciton as to the geometry and orbitals of the transition state. Then the prediction will be tested by optimising the transiiton state and comparing the prediction to results. We will also investigate the energy profile of the reaction, by optimising the reactants and products, and comparing their energies, and also comparing to the energy of the transition state.

Then, we look at the Diels Alder cycloaditon between Maleic anhydride acting ad the dienophile and 1,3Cyclohexadiene, exploring the regioselectivity of addition. Depending upon the orietation of the reactants, we can imagine two diasteroisomeric products, endo- and exo-product. We shall again use the principles of orbital symmetry conservation to explain which product we get, and demonstrate this by looking again at the reaction profile.

==Orbital Symmetry in the Diels Alder Reaction==

Pericyclic reactions are controlled by the symmetry of the frontier orbitals of the fragments reactning. We are going to predict whether this reaction is allowed, by using the Fukui method of reaction prediction (FO approach), which says that a filled HOMO mixes with an empty LUMO, stabilising the system, and forming a new sigma bond, but only if the orbitals can form symmetry allowed combinations. Hence, we shall visualise the FOs of the fragments, and determine which mixing is allowed.

So what are the frontier orbitals? Ethene is our archetypal pi system, featuring a pi homo and pi* LUMO. The HOMO is symmetirc with respect to a plane bisecting the molesule, and the LUMO is antisymmetric with respect to that same plane.

The HOMO of the cis-butadiene is also a pi system, with equal coefficients on both pi orbitals, since the two termini are equivalent. This orbital is antisymmetric with respect to a plane of symmetry bisecting the molecule The LUMO also is the pi* orbitals of the two double bonds, and is symmetric with respect to this plane.

<table border='1'>
<tr>
<td colspan='6'>
'''Frontier Orbitals of Ethene and cis-Butadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
Ethene HOMO
</td>
<td>
Ethene LUMO
</td>
<td rowspan='3'>
</td>
<td>
cis-Butadiene HOMO
</td>
<td>
cis-Butadiene LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Plot:'''
</td>
<td>
[[Image:pm08etheneHOMO.png|150px]]
</td>
<td>
[[Image:pm08etheneLUMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08cisbutadieneHOMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry w.r.t Plane:'''
</td>
<td>
'''S'''
</td>
<td>
'''A'''
</td>
<td>
'''A'''
</td>
<td>
'''S'''
</td>
</tr>
</table>

Orbitals of like symmetry can mix and form new sigma bonds, if one is empty and one is filled. Becuase of the symmetry constraint, the geomerty of approach is key, since only if the two orbitals approach each other so as to maintain their same-symmetry will we get reaction. The ethene LUMO and butadiene HOMO and both antisymmetric with respect to a plane of symmetry. Similarly, the butadiene LUMO and ethene HOMO and both symmetric with respect to the plane. Hence, given that these two reactants approach each other whilst maintaining that plane, the reaction is allowed, as the HOMO or one fragment can mix with the LUMO of the other, and form the new bonds.

We can now make a prediction as to the geometry of the transition state. As we have said, it has to keep the symmetry of the orbitals with respect to the plane bisecting the molecule. To form two new sigma bonds from pi bonds, we have to rehybrise sp2 to sp3, and we require the pi bonds of like phase in the transition state to approach end on. Hence, we can form two guesses as to the orbital picture in the transition state, from our symmetry allowed combinations of FOs , above. We couldn't make a guess as to which case we have without calculaiton, because these are both fairly 'electronically neutral' alkenes, i.e no electron puching or withdrawing substituents to shift the energy levels up or down.

[[Image:pm08DATSorbitalguess.png]]

Below, we discuss the method we used to optimise this transition state. But for the moment, let us jump ahead, and use the result of this transition state optimisation, to visualise the orbitals, and compare to our prediction. The HOMO of the transition state is symmetric with respect to the plane bisecting the molecule. Also, the molecular geometry respects this symmetry - the reaction would be disallowed in other geometries. Because it is S, we can show that the LUMO of the butadiene and the HOMO of the ethene mix. These must be the two FOs closest in energy, hence when they interact, they form the most stable bonding orbital. We see that the coefficients of the mixing orbitals have changed from those in the reactants. This is because the new bonds are part formed, so we see the cyclohexene pi bond forming, and the ethene pi bond and cis-butadiene pi bonds breaking, with increasing electron desity inbetween the two moelcules, where the sigma bonds are forming.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State HOMO'''
</td>
</tr>
<tr>
<td>
Computed Picture:
</td>
<td>
Guess:
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsALderTSHOMO1.png|150px]]
</td>
<td>
[[Image:pm08DATScorrectguess.png]]
</td>
</tr>
</table>

Comparing to our guess, we see that although the shapes of orbitals have changed, we can still determine the MO's which come together to react, which we correctly predicted based upon consideration of symmetry allowed FO combinsaions.

==Optimising reactants and product==

Compared to the Cope rearranegent, the Diels Alder reaction is Bimolecular and hence involves an unsymmetrical energy profile. We will, as before, first optimise the reactants and products, exploring their conformational preferences. The absolute energies of species discussed is presented in tables below. Energy changes will be discussed.

===Reactants===

[[Image:pm08Ethene.png|left]]
Ethene will only have one stable minimum, because necessarily it is planar. Minimising to DFT/B3LYP/6-31Gd level of theory, produced such a planar geometry with a C-C distance of 1.32A.

[[Image:pm08butadieneeqm.png|left]]
Butadiene is not so simple. Although the termini are fixed, by virtue of the double bonds, we can get rotation about the central C-C bond, resulting in different conformations, of which we would expect some to be minim and some transition states between them. To study the potential surface associated with rotation about that central dihedral, a SCAN calculation was carried out. Initially, the structure of cis-butadiene was optimised, initially HF 3-21G, then to DFT B3LYP 6-31G*. With the resulting geometry, using the redundant coordinate tool, the dihedral angle was defined, and set to scan 72 steps, in 5o intervals, ie a whole rotation from cis- to cis-butadiene. A relaxed-scan was then carried out to HF/3-21G theory. The plot of the energy profile, and maxima and minima structures for this bond rotation is shown below.

[[Image:pm08ButadieneDihedralScan.png|700px|right]]
Apart from the anomolous points, which must be due to poor optimisations, we obtain a symmetrical cuvre about the all trans (or about the all cis) conformer, i.e rotation in either direction is equivalent, as expected. The mimima and maxima were re-optimised to DFT B3LYP 6-31G*, which we use to discuss the energies. Starting at the trans conformer, we find it to be the most stable conformation. As the central bond is rotated, we reach a point where the dihedral is 90o, and a maximum in the energy profile, 7.56 kcalmol-1 higher in energy than the trans conformer. At 90o apart, the pi systems are orthogonal, so there can be no conjugation whatsoever. At 0o, the two pi systems are coplanar, so the amount of mixing would be at a maximum. Between these two extremes, the orbital overlap becomes less good, so less stabilised due to mixing, and so we see the total energy rise.

As the bond rotates further, we travel down a slope to find another minimum conformer, with a dihedral of 130o, which is 3.54 Kcalmol-1 higher in energy than the trans conformer. In this case, we have a balence of opposing interactions; orbital overlap increasing with increasing dihedral angle, but also steric bumping between vinyl protons increasing with increasing rotation. Hence, as the bond is further rotated, the orbital mixing increases, but so does steric bumping, and the steric repulsion is a stornger effect than the orbital mixing , so we see an energy rise, to another maximum, where the vinyl termini are co-planar, i.e the cis-isomer, which is infact a transition state, not a stable conformer, and is 3.88 kcalmol-1 higher in energy than the trans-conformer.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction Reactant Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Reactant'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Ethene
</td>
<td>
-78.58746
</td>
<td>
-49314.416
</td>
</tr>
<tr>
<td>
trans-butadiene
</td>
<td>
-155.99213
</td>
<td>
-97886.627
</td>
</tr>
<tr>
<td>
130o-Butadiene
</td>
<td>
-155.9864836
</td>
<td>
-97883.07832
</td>
</tr>
<tr>
<td>
cis-Butadiene
</td>
<td>
-155.9859496
</td>
<td>
-97882.74324
</td>
</tr>
<tr>
<td>
90o-Butadiene
</td>
<td>
-155.980091
</td>
<td>
-97879.06687
</td>
</tr>
</table>

===Product===

[[Image:pm08cyclohexene.png|left]]
We also expect cyclohexene to have several minima. Unfortunately, any potential surface scan to find conformations would be long and complex, because more than one bond rotation is required to convert between any minima. However from our knowledge of cyckohexane conformation, we can make some educated guesses as to what will be the stable minima , then we shall test our predictions by optimising to try to find these strutcures.

From our knowledge of cyclohexane conformation, but taking into account to geometry constraints imposd by the doubel bind, we can imagine two mimima conformations for cyclohexene, a half-chair and half-boat form. We will now perform optimisations
on guess-structures described to attempt to show this prediction to be true. A half-chair cyclohexene structure was created by taking chair-cyclohexane, and adjusting the bonds and valences as necessary. A hlaf oat structure was created by taking a bicyclo system, and removing one CH2CH2 group, and then adjusting bonding and valency. These guess structures were optimised initially to HF 3-21G theory, then the result to DFT B3LYP 6-31G*. As we predicted, these are both minima, and the half chair is indeed lower in energy, by 5.74 kcalmol-1.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels ALder Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Conformer'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Half-Chair Cyclohexene
</td>
<td>
-234.6482949
</td>
<td>
-147244.1516
</td>
</tr>
<tr>
<td>
Half-Boat Cyclohexene
</td>
<td>
-234.6391542
</td>
<td>
-147238.4157
</td>
</tr>
</table>

==Optimising the Transition State==

[[Image:pm08DielsAlderTS.png|left]]
To find the Transition state for our prototype Diels Alder Reaction, our optimised structures of ethene and cis-butadiene were taken, and added to one frame of a mol-group. The ethene was positioned above the plane of the cis-butadiene, in a geometry so when the QST 2 calcualtion interpolates the atomic positions between this starting point and optimised chair-cyclohexene, we would hope to find the expected transition state. The atomic labelling was changed between the two, so as to allow the atoms to map onto each other. This was run to HF 3-21G theory initially, then to DFT B3LYP 6-31G*. The resulting checkpoint file is shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Diels Alder Reaction QST2'''
</td>
</tr>
<tr>
<td>
Start Point
</td>
<td>
End Point
</td>
<td>
Result
</td>
</tr>
<tr>
<td>
[[Image:pm08DielsAlderQST2Start.png|200px]]
</td>
<td>
[[Image:pm08DielsAlderQST2End.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State</title><color>white</color><size>200</size>
<script>rotate;</script>
<uploadedFileContents>pm08DielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

Initially, the result looks quite a mess, but if we look at the vibrational frequencies we find we have an imaginary mode of magnitude 818cm<sup>-1</sup> in HF theury. When we changed to B3LYP theory, the energy of this mode was 525cm-1. Animating this mode, we find it is indeed the characteristic bond forming reaction. We found the transition state. Using Gaussview to clean the above structure, and animating this mode. The odd-bonding is just a relic of the interface. The fragments are positioned 2.21Å apart in the transition state.

<table border='1'>
<tr>
<td colspan='2'>
'''Diels Alder Transition State Cleaned Geometry and Imaginary Mode Animation'''
</td>
</tr>
<tr>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Cleaned up</title><color>white</color><size>250</size>
<script>measure 14 8; measure 12 1; rotate;</script>
<uploadedFileContents>pm08DielsAlderTSclean.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Transition State Imaginary Mode</title><color>white</color><size>250</size>
<script>frame 63;vectors 2;vectors scale 1;color vectors blue; vibration 2;
</script><uploadedFileContents>pm0834337.out</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
</table>

<table border='1'>
<tr>
<td>
'''Diels Alder Transition State Energy'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
'''DFT B3LYP 6-31G*'''
</td>
<td>
-234.5438966
</td>
<td>
-147178.6405
</td>
</tr>
</table>

==Following the reaction pathway==

Once the transition state had been found, an IRC calculation was carried out, to HF 3-21G theory. Unlike the Cope rearrangement of 1,5,hexadiene, the reaction profile is asymmetric, so we specified the calculation to travel in both directions, calculating the force constant at every step. Plotting the system electronic energy against reaction coordinate, we obtain the energy profile for the reaction.

[[Image:pm08DAIRC.png|700px|right]]
We see initially that the butadiene starts in a non-planar cis conformation, and he first necessary atomic displacement in the reaction is to become planar. Then the ethene approaches the pi system, where we see the hydrogen atoms bend back away from the forming bond. The product is in the half-boat conformation, which we said is a very high energy minima, only slightly lower than the transition state between half-chair and half-boat, so quickly we would expect the ring to rearrange to give the more stable half-chair conformer.

To calculate the activation energy for this reaction, and now, also the free energy of reaction, we need to reoptimiseour HF 3-21G results to DFT B3LYP 6-31G*, and then compare to the lowest energy (by convention) conformers of reactants and products. This will be the trans-butadiene and the half-chair cyclohexene. The calculated activation energy is 22.4 kcalmol-1. The calculated free eneergy change of reaction is -43.1 kcalmol-1.

=The Diels Alder Cycloaddition between 1,3-Cyclohexadiene and Maleic Anhydride: Regioselectivity=
==Orbital Symmetry==

Maleic Anhydride is an electron poor alkene, because the ester function withdraws electron density from the double bond. This results in the pi orbital, which in alkenes is normally our HOMO, being moved to HOMO-2, beacuse of the stabilising nature of the resonance with the ester. The HOMO is mostly carbonyl oxygen lone pair character.

<table border='1'>
<tr>
<td colspan='4'>
'''Maleic Anhydride'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO-2
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08maleicanhydrideHOMO-2.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideHOMO.png|150px]]
</td>
<td>
[[Image:pm08maleicanhydrideLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
S
</td>
<td>
A
</td>
<td>
A
</td>
</tr>
</table>

The 1,3-cyclohexadiene is a slightly electron rich diene, by virtue of electron pushing alkyl groups. However, when we look at the minimum energy conformer of 1,3-cyclohexadiene (puckered, see below), we find tat the molecule itself is not symmetric about a plane bisecting the molecule. Hence, its orbitals will not be either. In this case, we can say that to get a reaction, the diene must first become planar. Only then will mixing occur between that and maleic anhydride FOs, which is symmetric about a plane. Hence, we shall visualise the FOs of planar (the TS of the ring flip, see below) 1,3-cyclohexadiene, as this is the geometry to react, and treat the symmetry allowed combinations of these FO's. The orbitals are very much like the cis-butadiene orbitals, ie. The HOMO is of the two alkene pi orbitals, which is antisymmetric with respect to the plane, and the LUMO is pi* of the two double bonds, and is symmetric about the plane.

<table border='1'>
<tr>
<td colspan='4'>
'''Planar (TS of ring flip) 1,3-Cyclohexadiene'''
</td>
</tr>
<tr>
<td>
'''Orbital:'''
</td>
<td>
HOMO
</td>
<td>
LUMO
</td>
</tr>
<tr>
<td valign='top'>
'''Form:'''
</td>
<td>
[[Image:pm08planarcyclohexadieneHOMO.png|150px]]
</td>
<td>
[[Image:pm08planarcyclohexadieneLUMO.png|150px]]
</td>
</tr>
<tr>
<td>
'''Symmetry:'''
</td>
<td>
A
</td>
<td>
S
</td>
</tr>
</table>

This pair then and perfectly set up to react with the high energy diene HOMO overlapping with the low energy dienophile LUMO, i.e normal eectron demand. Comparing the symmetry of these FOs (planar cyclohexadiene), we find them to both be antisymmetric with respect to the plane. This is a symmetry allowed combination, and hence will result in a large stabilisation. We can form our guess of the transition state structure, again, with the dienophile approaching from a face-on, rather than end-on direction, so the pi/pi* orbitals meet end on. We now however, have an issue of regioselectivity. Before, there was no 'way around' for the ethene, whichever allowed orientation it approached in was the same. Now, the maleic anhydride can approach the diene in two orieations which abide to the symmetry of the plane. These lead to exo- and endo-isomers of te product adduct. We form our transition states guesses:

[[Image:pm08MADAorbitalguesses.png]]

And compare to the form of those computed:

[[Image:pm08MADAExoTSHOMO.png]]
[[Image:pm08MADAEndoTSHOMO.png]]

We see that they are indeed antisymmetric with respect to the plane. The form is complex, because, as we saw, the LUMO of the maleic anhydride was not simply pi* of the alkene, but also of the carbonyl.

We will also see that the endo transition state is lower in energy than the exo transition state. Above, we have drawn the FOs involved in the bond forming overlap, but we have neglected to consider what the other orbitals may be doing. The LUMO of the dienophile is also heavily carbonyl pi* in character, as well as the alkene pi*. In the endo-transition state, this pi system sits over the newly forming alkene, andthey can form a symmetry allowed combination. Because this is a HOMO/LUMO interation, the result is an overall stabilisation of the system. This secondary orbital overlap explains the observed endo-selectivity. The Exo-form has this pi system removed, so there can be no overlap.

==Optimising Reactants and Products==

We carry out our ordered procedure once more, initially optimising reactant and product geometries, initially to HF 3-21G, then to DFT B3LYP 6-31G*. Guess fragments were created using Gaussview 3.09, then optimising to theory. Once again, absolute energies given in a table below, energy chages discusesed. Optimisation to HF 3-21G initially, then to DFT B3LYP 6-31G*

[[Image:pm08MaleicAnhydride.png|left]]
Maleic Anhydride is necessarily planar, so there is not conformational freedom to concern us.

[[Image:pm0813cyclohexadiene.png|left]]
[[Image:pm0813cyclohexadieneringflip.png|right|700px]]
1,3-Cyclohexadiene could be either planar, which would maximise stabilising conjugation between the diene, but at the same time maximising staggering destabilising interactions in the CH2CH2 unit. Some puckering would reduce the staggering, but also the conjugation. We shall therefore form two guess structures for these conformers, and optimise. Creating a planar structure, and optimising from there, we receive a planar structure back. But analysis of the vibrations shows us that this is infact a transiton state we have found, by accident, with one imaginary mode of magnitude 154cm-1! Animating the vibration, we find that it is the puckering of the CH2Ch2 group to lower the staggering, as we discussed. Optimising to a puckered geometry, we find this to be a stable conformation. Running an IRC calculation starting from the planar transition state confirms that this leads to the puckered mimimum, with a symmetrical reaction profile, as expected, since puckering in either way is equivalent. The barrier to this ring flip is minimal, and easily passed with thermal energy.

[[Image:pm08MADAendoexo.png|left]]
There are two diastereoisomeric products, formed from different transition state geometries, which we will explore next. These are the endo- and exo- adducts. Guess fragments were created from a bicyclo fragment, and carbon tetrahedral fragments, then adjustign the bonding and valency accordingly in Gaussview, and these optimised. The two isomers are very similar in energy, with the endo-isomer being only 1.62 kcalmol-1 lower in energy than the exo-isomer. This is because the two products are very similar, but in the exo-isomer there is some small steric bumping between the CH2CH2 H atoms and the O atoms of the Maleic Anhydride fragment. The results are shown below.

<table border='1'>
<tr>
<td colspan='3'>
'''Reactant and Product Energies /DFT B3LYP 6-31G*'''
</td>
</tr>
<tr>
<td>
'''Molecule'''
</td>
<td>
'''Energy /Eh'''
</td>
<td>
'''Energy /kcalmol-1'''
</td>
</tr>
<tr>
<td>
Maleic Anhydride
</td>
<td>
-379.2895447
</td>
<td>
-238007.9822
</td>
</tr>
<tr>
<td>
Puckered 1,3-Cyclohexadiene
</td>
<td>
-233.4189323
</td>
<td>
-146472.7142
</td>
</tr>
<tr>
<td>
Planar 1,3-Cyclohexadiene TS
</td>
<td>

</td>
<td>

</td>
</tr>
<tr>
<td>
Endo-Product Isomer
</td>
<td>
-612.7582899
</td>
<td>
-384511.9545
</td>
</tr>
<tr>
<td>
Exo-Product Isomer
</td>
<td>
-612.7557845
</td>
<td>
-384510.3823
</td>
</tr>
</table>

==Optimising Transition States==

As we did for the Butadiene/Ethene Diels Alder cycloaddition, a QST2 TS opt was used to find the two transition states. A guess geometry was created for the start piont, to allow the interpolation between this structure and the corresponding product isomer to give the transititon state. A molgroup was created, and the numbering changed accordingly.

<table border='1'>
<tr>
<td colspan='4'>
'''Diels Alder Reaction between Maleic Anhydride and 1,3-Cyclohexadiene QST2 '''
</td>
</tr>
<tr>
<td></td>
<td>
'''Starting Point'''
</td>
<td>
'''End Point'''
</td>
<td>
'''Result'''
</td>
</tr>
<tr>
<td valign='top'>
'''Exo-Isomer'''
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08exoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Exo TS</title><color>white</color><size>200</size>
<script>measure 5 20; measure 2 18; rotate;</script>
<uploadedFileContents>pm08exoMADielsAlderTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>
</td>
</tr>
<tr>
<td valign='top'>
'''Endo-Isomer'''
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2start.png|200px]]
</td>
<td>
[[Image:pm08endoMAdielsAlderQST2end.png|200px]]
</td>
<td>
<jmol>
<jmolApplet>
<title>Diels Alder Maleic Anhydride Endo TS</title><color>white</color><size>200</size>
<script>measure 5 18; measure 2 20; rotate;</script>
<uploadedFileContents>pm08MADielsAlderEndoTS.mol</uploadedFileContents>
</jmolApplet>
</jmol>

</td>
</tr>
</table>

==Following the reaction pathway==
[[Image:pm08MADAIRC.png|700px|right]]
[[Image:pm08MAExoDAIRC.png|700px|right]]
[[Image:pm08MADApathwaysenergy.png|700px|right]]
On the structures found to be transition states from the QST2 calculation, an IRC calculation was carried out to HF 3-21G theory, for each diastereoisomer. The resulting reaction profiles are shown below.

Initially, to react, the puckered 1,3-cyclohexadiene has to become planar, which we saw is a transition state for the ring flip, which requires a rise in energy, seen in the plot. As the reactants move together, the energy quickly rises, due to steric and electeonic repulsion. We see that the exo transition state is at a higher energy than the endo transition state. The product energies are almost comparable, as we saw, but the endo-isomer is very slightly lower. Becuase the endo transition state is lower in energy and the product has a lower energy, the endo-isomer is both the kinetic and thermodynamic product of this reaction.

All that remains to be done is to reoptimise our transition states and reacctnats and products to DFT B3LYOP 6-31G* to report a calculated activation energy and free energy of reaction. The activation energy for the Endo pathway is calcuated at 15.74 kcalmol-1. That for the exo pathway is calculated at 18.30 kcalmol-1. This explains the endo-selectivity under kinetic reaction conditions. The free energy change on reaction for the endo pathway is calculated to be -31.26 kcalmol-1. That for the exo-pathwas is at -29.69 kcalmol-1. Hence, the endo pathway is also favoured under theromdynamic conditions.
</div>
----

[[Mod:atbxz79361|Index]]

[[Mod:atbxz79362|The Cope Rearrangement]]

[[Mod:atbxz79363|The Diels Alder Cycloaddition]]

[[Mod:atbxz79364|The Pathway to Adamantane...]]

----