2012-02-17T14:49:36Z

Ab3609: /* Boat Transition Structure */

==The Cope Rearrangement==

Sigmatropic rearrangements are a pericyclic reaction in which a σ-bonds is changed to another through an intramolecular process. An example of a sigmatropic reaction is the [3,3]-Cope rearrangement.

[[File:Cope_mech_ab.gif|thumb|center|Cope rearrangement]]

1,5-hexadiene can undergo a Cope rearrangement via a "chair" or "boat" transition structure. The "boat" transition structure is meant to be higher in energy than the "chair" structure. This will be analyzed using GuassView below.

[[File:Chairboatts_ab.gif|thumb|center|Chair and Boat Transition structures]]

===Optimisating reactants and products===

Initially the reactants and products were made drawn and optimised in GuassView and these calculations can be compared to the experimental values. A molecule of 1,5-hexadiene can be in either the 'anti' or 'gauche' conformation depending on the arrangement of the middle four carbons (C2-C3-C4-C5). All conformers were optimised using Hartree-Fock, 3-21G method.

[[File:1,5-hex.gif|thumb|center|500px|1,5-hexadiene]]

====Antiperiplanar====

A molecule of 1,5-hexadiene was drawn out in GuassView with an 'anti' linkage across the central four carbons. The optimised molecule was then compared to the molecules in the index to deduce which conformer had been produced.

[[Image:15_app_ab.JPG|thumb|center|150px|'Anti' linkage 
<jmol>
<jmolAppletButton>
<uploadedFileContents>App_diene_opt_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000166 0.001200 YES
Predicted change in Energy=-1.183326D-08
Optimization completed.
-- Stationary point found.

''Symmetry''

Point group= C2h

====Gauche====

[[Image:15_gauche_ab.JPG|thumb|center|150px|'Gauche' linkage 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Gauche_diene_opt_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000672 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-2.586982D-08
Optimization completed.
-- Stationary point found.

''Symmetry''

Point group= C2

''Alternative gauche conformer''

The dihedral angle can be altered to give a different gauche conformer with C2 symmetry:

[[Image:15_gauche2.JPG|thumb|center|150px|Alternative 'Gauche' linkage 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Gauche2_diene_opt.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

====Ci Anti2====

[[Image:15_ci_ab.JPG|thumb|center|150px|Ci anti2 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Ci_opt_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

Item Value Threshold Converged?
Maximum Force 0.000047 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000599 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-2.590044D-08
Optimization completed.
-- Stationary point found.

''B3YLP/6-31G''

The optimised Ci structure was reoptimised using B3LYP/6-31G* method and compared to the HF/3-21G structure.

[[Image:Ci_b3lyp_ab.JPG|thumb|center|150px|Ci optimised using B3LYP/6-31G* 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Ci_b3lyp_freq_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

Energy of Ci conformer (B3LYP/6-31G*)= -234.62319422

Energy of Ci conformer (HF/3-21G)= -231.69254

Geometry changed...

====Summary of conformers====

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''Conformer'''
| align="center" style="background:#f0f0f0;"|'''Structure'''
| align="center" style="background:#f0f0f0;"|'''Point group'''
| align="center" style="background:#f0f0f0;"|'''Energy (Hartrees)'''
| align="center" style="background:#f0f0f0;"|'''Relative energy (kcal)'''
| align="center" style="background:#f0f0f0;"|'''Appendix value'''
|-
| gauche1||[[File:15_gauche_ab.JPG|center|200px]]||C2||-231.68772||3.1||-231.68772
|-
| gauche2||[[File:15_gauche2.JPG|center|200px]]||C2||-231.69167||0.62||-231.69167
|-
| anti2||[[File:15_ci_ab.JPG|center|200px]]||Ci||-231.69254||0.08||-231.69254
|-
| anti3||[[File:15_app_ab.JPG|center|200px]]||C2h||-231.68907||2.25||-231.68907
|-
|
|}

====Vibrational analysis====

Additional frequency calculations need to be carried out in order to be able to compare the energies with experimental quantities. The optimised B2LYP/6-31G* structure was used to run the frequency calculations. The thermochemistry results from the output file can be seen below:

Sum of electronic and zero-point Energies (E=Eelec+ ZPE)= -234.481064
Sum of electronic and thermal Energies (E= E+ Evib+ Erot+ Etrans)= -234.473713
Sum of electronic and thermal Enthalpies (H= E+ RT)= -234.472768
Sum of electronic and thermal Free Energies (G= H- TS)= -234.512636

===Optimising the "Chair" and "Boat" Transition Structures===

The transition structures for the 'chair' and 'boat' conformations are both drawn by using two C3H5 allyl fragments and optimised using three different methods, all of which will be explored in turn below.

====Chair Transition Structure====

A guess structure was drawn in GuassView and used as the starting point for the calculations. The distance between the two allyl fragments was set to roughly 2.2Å. Transition state calculations involve finding the negative direction of the curvature and can be worked out most accurately using force constants, however this will not work if the guess structure is significantly different to the transition structure. In this situation, it is better to use the freeze coordination method which allows the rest of the molecule to relax first and then finds the transition state.

The Guess structure was optimised to a Transition State (Berny) using Hartree Fock and 3-21G basis set.{{DOI|10042/to-12412}}

[[File:Chair_partb.gif|thumb|center|250px|Vibration of the chair structure at the imaginary frequency]]

One '''imaginary frequency of -817.96cm-1''' with an intensity of 5.87. As seen from the above animation, this imaginary frequency directly relates to the cope rearrangement with the formation of one σ bond whilst simultaneously breaking the other σ bond.

'''Freeze Coordinate method'''

The transition strusture can also be optimised using the freeze coordinate method. The guess structure was opened in a new file on GuassView, the bond between the new bond forming carbons were frozen at 2.2Å and then optimised using HF/3-21G. This step allows the rest of the atoms to relax whilst freezing the terminal carbons are frozen in their place.

The fchk output file of this is then optimised further by changing the frozen bonds into derivates, therefore allowing them to move so they can form the optimum transition structure. This transition structure was compared to the one worked out using the force constants method, a summary of which can be seen below:

{| class=wikitable
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Force constant method'''
| align="center" style="background:#f0f0f0;"|'''Freeze coord. Method'''
|-
| Energy (Hartrees)||-231.61932||-231.61932
|-
| Gradient (Hartrees)||0.00001022||0.0000549
|-
| Terminal bond distance||2.02029||2.0199
|-
| Structure||<jmolFile text="Jmol">Chair_forcec_ab.mol</jmolFile>||<jmolFile text="Jmol">Chair_d2_ab.mol</jmolFile>
|-
|
|}
From the table above, it can be deduced that the energies are very similar, however there is a difference in the terminal C-C length. The force constant method produces a larger difference between these carbons, however has a lower gradient therefore a more accurate representation of the transition structure. However the force constant method can not always be used for larger molecules.

====Boat Transition Structure====

The boat transition structure is optimised using the QST2 method. The involves specifying the reactants and products by numbering them specifically and then the program with find a structure between the two. The original Ci reactant molecule was used to create the reactant and product. Opt+Freq calculations were then carried out on this molecule using the TS(QST2) option. The result of this calculation shows the molecule below which is obviously incorrect.

[[File:Boat_fail_ab.JPG|thumb|center|200px|Boat job fails]]

This is because the program does not consider the ability to rotate around the central C-C bond. Therefore, if we go back and change the dihedral angle for C2-C3-C4-C5 to 0° and then change the angles between C2-C3-C4 and C3-C4-C5 angles to 100° for both the reactant and products and re-run the TS(QST2) calculation the Transition state should be found. {{DOI|10042/to-12419}}

[[Image:Boat_qst2_ab.JPG|thumb|center|150px|Boat TS(QST2) 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Boat_rot1_ab1.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

====IRC====

The '''Intrinsic Reaction Coordinate''' method is a method which allows you to follow the potential energy surface for the minimum energy path from the transition structure to the local minimum.

=====Chair=====

The optimised chair transition structure was opened in GuassView. As the reaction is symmetrical, only the forward direction is calculated. The number of points on the IRC curve was increased to 50 and the IRC calculations were run. The resulting output file was opened and the structure was compared to that of the gauche2 conformer.

[[File:Chair_irc26_ab.gif|thumb|center|250px|Animation showing the 26 points along the IRC]]

[[File:Chair_irc1_ab.jpg|thumb|center|300px|IRC graph1]]
[[File:Chair_irc2_ab.jpg|thumb|center|300px|IRC graph2]]

From the graphs above it can be seen that the progression of the points along the IRC leads to a structure with low energy and a gradient close to zero. This relates to the local minimum and is reached by taking steps in the direction with the steepest gradient. Initially the energy drops rapidly until small changes to the structure result in slightly lower energies. The summary of the lowest energy structure can be seen below.

[[File:Summary_chair_irc_ab.JPG|thumb|center|400px|Summary for IRC]]

'''IRC opt'''

The final structure from the IRC above may not be the one with the minimum geometry therefore this molecule can then be optimised further using the three different methods explored below.

''(i) The last point of the IRC is minimised''

The last point of the IRC was taken and optimised using Hartree-Fock method with 3-21G basis set. The resulting molecule had C2 symmetry, therefore it can be related to the gauche2 structure in the reactants and products table above. The energy of this minimum is -231.69167 Hartrees, this value directly links to the appendix value (-231.69167) therefore it can be assumed that the minimum reached is of the gauche2 conformation.

[[Image:Opt_irc26_ab.JPG|thumb|center|150px|Optimised structure 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Opt_irc26_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

[[File:Summary_opt_irc26_ab.JPG|thumb|center|400px|Summary for minimised structure of IRC 26]]

A disadvantage of this method is that one can not be sure if the correct minimum has been reached. This is due to the fact that this calculation will take you to the closest minimum which may not always be the lowest minimum.

''(ii) Increasing the number of points on the IRC''

The second method of optimising involved increasing the number of points on the IRC curve. This can be done in an effort to increase the number of points thus allowing a minimum to be reached. However only 26 points were found on the output file and the same geometry of the molecule was given. The energy for this molecule can be compared to the energy of the IRC carried out initially and both give the same total energy of -231.68828 Hartrees.

[[File:Irc_chair_opt100_ab.gif|thumb|center|250px|Animation of the intermediates]]

[[File:Summary_irc100_chair_ab.JPG|thumb|centre|400px|Summary for IRC increased to 100 points]]

''(iii) Compute force constants at every step''

This method involved computing force constants at every step. This is the most reliable method that can be used, however this method may not work for larger systems as it will take a long time.

[[File:Chair_ircfc_ab.gif|thumb|center|250px|Animation of the intermediate geometries]]

[[File:Chair_ircfc1_ab.jpg|thumb|center|300px|IRC graph1]]
[[File:Chair_ircfc2_ab.jpg|thumb|center|300px|IRC graph2]]

The above graphs show the points along the energy curve until the minimum was reached. However on the graph about the gradient, a slight incline is seen at the last point. This could correlate to the fact that the physical representation of a bond is removed between the 47th and 48th point. This may lead to a slight increase in energy towards the end of the curve. The energy for this method (-231.69166 Hartrees) is roughly similar to the energy obtained in method (i) (-231.69167) which suggests that a similar minimum has been achieved whereas the IRC and method (ii) produced a different minimum.

[[File:Summary_opt_ircfc_chair_ab.JPG|thumb|centre|400px|Summary for IRC using force constants]]

=====Boat=====

A similar method was carried out on the Boat conformer in an aim to reach the local minimum. However the methods below have lead to the formation of a minimum which is not the correct minimum, the geometry reached is similar to the conformation of gauche2. If time permited, these calculations could be re-done to try and figure out why the correct minimum was not reached.

[[File:Boat_irc_ab.gif|thumb|center|250px|Animation of intermediate boat geometries]]

[[File:Boat_irc_ab.jpg|thumb|center|300px|IRC graph1]]
[[File:Boat_irc1_ab.jpg|thumb|center|300px|IRC graph2]]

[[File:Summar_boat_irc_ab.JPG|thumb|centre|400px|Summary for IRC]]

'''IRC Opt'''

''(i) The last point of the IRC is minimised''

[[Image:Boat_ircopt_ab.JPG|thumb|centre|150px|Optimised structure 
<jmol>
<jmolAppletButton>
<uploadedFileContents>B_irc_opt20_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

[[File:Summary_boat_ircopt_ab.JPG|thumb|centre|400px|Summary]]

''(ii) Increasing the number of points on the IRC''

[[File:Boat_irc100_ab.JPG|thumb|centre|200px|Structure of final point on 100 point IRC]]

[[File:Summary_boat_irc100_ab.JPG|thumb|centre|400px|Summary for IRC increased to 100 points]]

''(iii) Compute force constants at every step''

[[File:Boat_ircfc_anim_ab.gif|thumb|center|250px|Animation of the intermediate geometries]]

[[File:Boat_ircfc_graph1_ab.jpg|thumb|center|300px|IRC graph1]]
[[File:Boat_ircfc_graph2_ab.jpg|thumb|center|300px|IRC graph2]]

[[File:Summary_boat_ircfc_ab.JPG|thumb|centre|400px|Summary for IRC using force constants]]

====Activation energy====

Further activation energy calculations were carried out by optimising the transition structures to a TS (Berny) using B3LYP method with a 6-31G* basis set. The ''Thermochemistry'' data was then taken from the output files of these molecules and compared to the Anti2 (Ci) conformation to show the energy required to get from the reactant to the transition state. The full analysis of this can be seen in the table below.

Boat structure: {{DOI|10042/to-12578}}
Chair structure: {{DOI|10042/to-12582}}

{| class=wikitable
|-
|'''B3LYP/6-31G* (Hartrees)'''
|'''Anti2(Ci)'''
|'''Boat TS'''
|'''Chair TS'''
|'''Difference (boat) (kcal/mol)'''
|'''Difference (chair) (kcal/mol)'''
|-
| Total Energy
| -234.62319
| -234.55445
| -234.56752
| 43.14
| 34.93
|-
| Zero-point energy
| -234.41064
| -234.414235
| -234.425905
| 2.26
| 9.58
|-
| Thermal energies
| -234.4737
| -234.407819
| -234.419926
| 41.35
| 33.75
|}

The values in the table above can be compares to experimental values: 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. The calculated energies match the literature values therefore showing that the chair transition structure has a lower activation energy therefore the reaction will proceed via this route.

==Diels Alder Cycloaddition reaction==

The Diels Alder Cycloaddition reaction is known as a type of pericyclic reaction between a diene and a dienophile to form a cyclohexene system. The π orbitals on the dienophile form new σ bonds with the π orbital from the diene. Usually if the HOMO of one interacts with the LUMO of the other than the cycloaddition is allowed, however both molecular orbitals need to have the same symmetry otherwise there will be no overlap and therefore the reaction will not proceed.
The ''Cis principle'' <ref name=Sauer>
J. Sauer,
''Diels-Alder reactions II: The reaction mechanism'',
'''1967''',
17,
{{DOI|10.1002/anie.196700161}} </ref> states that the stereochemistry of the reactants is maintained in the product and therefore the subsituents will be on the same face of the ring in the product. The maleic anhydride example below shows this, however the cis substituents are part of a ring and are therefore on the same face due to steric lock.

===Butadiene and Ethylene===

Butadiene and Ethylene can undergo a [4+2]- Cycloaddition to form cyclohexene. The reaction involves the interaction between the HOMO and LUMO's of Butadiene and Ethylene as seen below.

[[File:Homolumobutadiene_ab.gif|thumb|center|300px|HOMO and LUMO interactions]]

These LCAO's represent the interaction between the π and π* orbitals of the reactants. The Molecular orbitals obtained from the calculations will prove these interactions.

====Optimising butadiene====

A molecule of butadiene was drawn in GaussView and optimised using the Semi-empirical molecular orbital method with the AM1 basis set. Cis butadiene is used to ensure maximum orbital overlap is achieved.

[[Image:Butadiene_opt_am1_ab.JPG|thumb|center|150px|The structure of AM1 optimised cis-butadiene 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Butadiene_opt_am1_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

'''HOMO- LUMO'''

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''MO'''
| align="center" style="background:#f0f0f0;"|'''Image'''
| align="center" style="background:#f0f0f0;"|'''LCAO'''
| align="center" style="background:#f0f0f0;"|'''Symmetry'''
|-
| HOMO||[[File:Homoe_butadiene_ab.jpg|150px]]||[[File:Homolcao_butadiene_ab.gif|150px]]||anti-symmetric
|-
| LUMO||[[File:Lumo_butadiene_ab.jpg|150px]]||[[File:Lumolcao_butadiene_ab.gif|150px]]||symmetric
|-
|
|}

====Transition State geometry====

The ethylene approaches the cis butadiene from above, in an aim to maximum the overlap between the π orbitals.

[[Image:42_ts_ab.JPG|thumb|center|150px|Transition structure with C-C bond lengths 
<jmol>
<jmolAppletButton>
<uploadedFileContents>42_optfreq_am1_ab.mol</uploadedFileContents>
<script> measure 5 14; measure 8 11 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

The bond lengths visible in the Jmol above shows the σ bond lengths of the partially formed C-C bonds. The typical Csp3-sp3 in cyclohexane is 1.535Å<ref name=Allen>
Frank H. Allen, Olga Kennard and David G. Watson,
''J. Chem. Soc. Perkin Trans. II'',
'''1987''',
S6-S7</ref>, and the typical Csp2-Csp2 bond length is 1.455<ref name=Allen>
Frank H. Allen, Olga Kennard and David G. Watson,
''J. Chem. Soc. Perkin Trans. II'',
'''1987''',
S6-S7</ref>. Therefore it can be seen that the partially formed σ bond is much longer than both of these lengths as it is not yet a bond, however once formed it will relate most to the Csp3-sp3 length. The Van der Waals radius for carbon is 1.7Å<ref name=Bondi>
A. Bondi,
''J. Phys. Chem.'',
'''1964''',
448,
{{DOI|10.1021/j100785a001}} </ref>, therefore it can be deduced that the distance is shorter than a Van der Waals interaction but not close enough to be a σ bond, therefore an intermediate stage has been reached.

The optimised transition state had an imaginary frequency at -956.14cm-1, this relates to the formation of the new σ-bonds which is synchronous.

[[File:Imaginaryfreq_ts_da_ab.gif|thumb|centre|250px|Animation of imaginary frequency]]

This can then be compared tot he frequency of the lowest positive vibration at 147.29cm-1, which shows an asynchronous movement and does not relate to the formation of the new σ bonds.

[[File:Lowestpos_ab.gif|thumb|centre|250px|Animation of lowest frequency]]

'''HOMO-LUMO'''

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [[File:Homo_ts_da_ab.jpg|thumb|center|150px|HOMO]]||[[File:Lumo_ts_da_ab.jpg|thumb|center|150px|LUMO]]
|-
| Anti-symmetric||Symmetric
|-
|
|}

The above diagrams show a molecular orbital representation of the π/ π* interaction of ethylene and the HOMO/LUMO of butadiene. The reaction is [4s + 2s] due to the fact that butadiene has 4 π orbitals in the π system and ehtylene has 2 π orbitals. The molecular orbitals of ethylene and butadiene have been labelled as symmetric and anti-symmetric with respect to the middle plane. The reason this reaction is allowed is because the HOMO of one interacts with the LUMO of the other, therefore it can be seen that the molecular orbitals of the transition state match the LCAO's predicted before the calculations were carried out.

===Cyclohexa-1,3-diene reaction with Maleic Anhydride===

This exercise aims to prove the fact that the cycloaddition reaction between cyclohexa-1,3-diene and maleic anhydride results in the primarily formation of the endo structure. This is due to the fact that the endo structure is lower in energy therefore the reaction is kinetically controlled resulting in a regioselective reaction.

[[File:Exoendoma_ab.gif|thumb|center|500px|Reaction of cyclohexa-1,3-diene and maleic anhydride to form the exo and endo adducts]]

====Exo Tranition structure====

The exo and endo structures were calculated using the freeze coordination method. The cyclohexa-1,3-diene were optimised separately and then a guess structure of the transition state was made. The distance between the two carbons forming the new bonds were frozen at 2.2Å and then optimised using HF/3-21G. This step allows the rest of the atoms to relax whilst freezing the reacting carbons in their place.

The output file of this structure was optimised further by using derivate bonds, thus allowing them to move to form the optimum transition structure:

[[Image:P3_exo_ab.JPG|thumb|center|150px|Exo transition state 
<jmol>
<jmolAppletButton>
<uploadedFileContents>P3_exo_ab.mol</uploadedFileContents>
<script> measure 1 16; measure 4 17 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

This structure also displayed an imaginary frequency at -647.42cm-1 with an intensity of 67.5. From the animation below it can be seen that this vibration links directly to the formation of the new σ-bonds.

[[File:Ma_im_exo_ab.gif|thumb|centre|250px|Animation of imaginary frequency]]

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [[File:Homo_exo1_ma_ab.jpg|thumb|center|150px|Homo for the exo structure]]||[[File:Lumo_exo1_ma_ab.jpg|thumb|center|150px|Lumo for the exo structure]]
|-
|
|}

====Endo Transition structure====

The endo transition structure was calculated using the same method as the exo structure.

[[Image:P3_endo_ab.JPG|thumb|center|150px|Endo transition state 
<jmol>
<jmolAppletButton>
<uploadedFileContents>P3_endo_ab.mol</uploadedFileContents>
<script> measure 1 17; measure 4 16 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [[File:Homo_endo_ma_ab.jpg|thumb|center|200px|Homo for the endo structure]]||[[File:Lumo_endo_ma_ab.jpg|thumb|center|200px|Lumo for the endo structure]]
|-
|
|}

====Comparison between endo and exo transition states====

{| class=wikitable
|
|'''exo'''
|'''endo'''
|-
|Method
|HF/3-21G
|HF/3-21G
|-
| Energy (Hartrees)
| -605.60352
| -605.61037
|}

From the above table it can be seen that the endo structure is more stable as it is lower in energy by 0.00685 Hartrees (4.3 Kcal/mol). This agrees with the statement made at the state that the endo structure was predominately formed due to the fact that the reaction proceeded due to kinetics.

The exo structure is higher in energy due to the strain between the carbonyl cabons and the cyclohexa-1,3-diene ring, which are 2.92Å apart. The steric disterence in the endo structure is much closer at 2.8Å, this may lead one to assume that the endo structure is not favored.

However, this reaction is not controlled by such sterics. The main factor that controls the stereochemistry is the secondary orbital interaction<ref name=Fox>
Maryne Anne Fox, Raul Cardona, Nicoline J. Kiwiet,
''Journal of Organic Chemistry'',
'''1987''',
1469-1470,
{{DOI|10.1021/jo00384a016}} </ref>. From the MO's above it can be seen that there is significantly more secondary orbital overlap in the endo structure compared to the exo structure. The LCAO's below show the extent overlap in a much clearer way. The increase in overlap stabilises the endo structure.

[[File:Secondary_overlap_ab.gif|thumb|center|500px|Secondary orbital overlap]]

==References==
<references/>

2012-02-17T12:15:55Z

Ab3609: /* Comparison between endo and exo transition states */

==The Cope Rearrangement==

Sigmatropic rearrangements are a pericyclic reaction in which a σ-bonds is changed to another through an intramolecular process. An example of a sigmatropic reaction is the [3,3]-Cope rearrangement.

[[File:Cope_mech_ab.gif|thumb|center|Cope rearrangement]]

1,5-hexadiene can undergo a Cope rearrangement via a "chair" or "boat" transition structure. The "boat" transition structure is meant to be higher in energy than the "chair" structure. This will be analyzed using GuassView below.

[[File:Chairboatts_ab.gif|thumb|center|Chair and Boat Transition structures]]

===Optimisating reactants and products===

Initially the reactants and products were made drawn and optimised in GuassView and these calculations can be compared to the experimental values. A molecule of 1,5-hexadiene can be in either the 'anti' or 'gauche' conformation depending on the arrangement of the middle four carbons (C2-C3-C4-C5). All conformers were optimised using Hartree-Fock, 3-21G method.

[[File:1,5-hex.gif|thumb|center|500px|1,5-hexadiene]]

====Antiperiplanar====

A molecule of 1,5-hexadiene was drawn out in GuassView with an 'anti' linkage across the central four carbons. The optimised molecule was then compared to the molecules in the index to deduce which conformer had been produced.

[[Image:15_app_ab.JPG|thumb|center|150px|'Anti' linkage 
<jmol>
<jmolAppletButton>
<uploadedFileContents>App_diene_opt_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000166 0.001200 YES
Predicted change in Energy=-1.183326D-08
Optimization completed.
-- Stationary point found.

''Symmetry''

Point group= C2h

====Gauche====

[[Image:15_gauche_ab.JPG|thumb|center|150px|'Gauche' linkage 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Gauche_diene_opt_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
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Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000672 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-2.586982D-08
Optimization completed.
-- Stationary point found.

''Symmetry''

Point group= C2

''Alternative gauche conformer''

The dihedral angle can be altered to give a different gauche conformer with C2 symmetry:

[[Image:15_gauche2.JPG|thumb|center|150px|Alternative 'Gauche' linkage 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Gauche2_diene_opt.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

====Ci Anti2====

[[Image:15_ci_ab.JPG|thumb|center|150px|Ci anti2 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Ci_opt_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
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Item Value Threshold Converged?
Maximum Force 0.000047 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000599 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-2.590044D-08
Optimization completed.
-- Stationary point found.

''B3YLP/6-31G''

The optimised Ci structure was reoptimised using B3LYP/6-31G* method and compared to the HF/3-21G structure.

[[Image:Ci_b3lyp_ab.JPG|thumb|center|150px|Ci optimised using B3LYP/6-31G* 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Ci_b3lyp_freq_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

Energy of Ci conformer (B3LYP/6-31G*)= -234.62319422

Energy of Ci conformer (HF/3-21G)= -231.69254

Geometry changed...

====Summary of conformers====

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''Conformer'''
| align="center" style="background:#f0f0f0;"|'''Structure'''
| align="center" style="background:#f0f0f0;"|'''Point group'''
| align="center" style="background:#f0f0f0;"|'''Energy (Hartrees)'''
| align="center" style="background:#f0f0f0;"|'''Relative energy (kcal)'''
| align="center" style="background:#f0f0f0;"|'''Appendix value'''
|-
| gauche1||[[File:15_gauche_ab.JPG|center|200px]]||C2||-231.68772||3.1||-231.68772
|-
| gauche2||[[File:15_gauche2.JPG|center|200px]]||C2||-231.69167||0.62||-231.69167
|-
| anti2||[[File:15_ci_ab.JPG|center|200px]]||Ci||-231.69254||0.08||-231.69254
|-
| anti3||[[File:15_app_ab.JPG|center|200px]]||C2h||-231.68907||2.25||-231.68907
|-
|
|}

====Vibrational analysis====

Additional frequency calculations need to be carried out in order to be able to compare the energies with experimental quantities. The optimised B2LYP/6-31G* structure was used to run the frequency calculations. The thermochemistry results from the output file can be seen below:

Sum of electronic and zero-point Energies (E=Eelec+ ZPE)= -234.481064
Sum of electronic and thermal Energies (E= E+ Evib+ Erot+ Etrans)= -234.473713
Sum of electronic and thermal Enthalpies (H= E+ RT)= -234.472768
Sum of electronic and thermal Free Energies (G= H- TS)= -234.512636

===Optimising the "Chair" and "Boat" Transition Structures===

The transition structures for the 'chair' and 'boat' conformations are both drawn by using two C3H5 allyl fragments and optimised using three different methods, all of which will be explored in turn below.

====Chair Transition Structure====

A guess structure was drawn in GuassView and used as the starting point for the calculations. The distance between the two allyl fragments was set to roughly 2.2Å. Transition state calculations involve finding the negative direction of the curvature and can be worked out most accurately using force constants, however this will not work if the guess structure is significantly different to the transition structure. In this situation, it is better to use the freeze coordination method which allows the rest of the molecule to relax first and then finds the transition state.

The Guess structure was optimised to a Transition State (Berny) using Hartree Fock and 3-21G basis set.{{DOI|10042/to-12412}}

[[File:Chair_partb.gif|thumb|center|250px|Vibration of the chair structure at the imaginary frequency]]

One '''imaginary frequency of -817.96cm-1''' with an intensity of 5.87. As seen from the above animation, this imaginary frequency directly relates to the cope rearrangement with the formation of one σ bond whilst simultaneously breaking the other σ bond.

'''Freeze Coordinate method'''

The transition strusture can also be optimised using the freeze coordinate method. The guess structure was opened in a new file on GuassView, the bond between the new bond forming carbons were frozen at 2.2Å and then optimised using HF/3-21G. This step allows the rest of the atoms to relax whilst freezing the terminal carbons are frozen in their place.

The fchk output file of this is then optimised further by changing the frozen bonds into derivates, therefore allowing them to move so they can form the optimum transition structure. This transition structure was compared to the one worked out using the force constants method, a summary of which can be seen below:

{| class=wikitable
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Force constant method'''
| align="center" style="background:#f0f0f0;"|'''Freeze coord. Method'''
|-
| Energy (Hartrees)||-231.61932||-231.61932
|-
| Gradient (Hartrees)||0.00001022||0.0000549
|-
| Terminal bond distance||2.02029||2.0199
|-
| Structure||<jmolFile text="Jmol">Chair_forcec_ab.mol</jmolFile>||<jmolFile text="Jmol">Chair_d2_ab.mol</jmolFile>
|-
|
|}
From the table above, it can be deduced that the energies are very similar, however there is a difference in the terminal C-C length. The force constant method produces a larger difference between these carbons, however has a lower gradient therefore a more accurate representation of the transition structure. However the force constant method can not always be used for larger molecules.

====Boat Transition Structure====

The boat transition structure is optimised using the QST2 method. The involves specifying the reactants and products by numbering them specifically and then the program with find a structure between the two. The original Ci reactant molecule was used to create the reactant and product. Opt+Freq calculations were then carried out on this molecule using the TS(QST2) option. The result of this calculation shows the molecule below which is obviously incorrect.

[[File:Boat_fail_ab.JPG|thumb|center|200px|Boat job fails]]

This is because the program does not consider the ability to rotate around the central C-C bond. Therefore, if we go back and change the dihedral angle for C2-C3-C4-C5 to 0° and then change the angles between C2-C3-C4 and C3-C4-C5 angles to 100° for both the reactant and products and re-run the TS(QST2) calculation the Transition state should be found. {{DOI|10042/to-12419}}

[[Image:Boat_qst2_ab.JPG|thumb|center|150px|Boat TS(QST2) 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Boat_qst2_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

====IRC====

The '''Intrinsic Reaction Coordinate''' method is a method which allows you to follow the potential energy surface for the minimum energy path from the transition structure to the local minimum.

=====Chair=====

The optimised chair transition structure was opened in GuassView. As the reaction is symmetrical, only the forward direction is calculated. The number of points on the IRC curve was increased to 50 and the IRC calculations were run. The resulting output file was opened and the structure was compared to that of the gauche2 conformer.

[[File:Chair_irc26_ab.gif|thumb|center|250px|Animation showing the 26 points along the IRC]]

[[File:Chair_irc1_ab.jpg|thumb|center|300px|IRC graph1]]
[[File:Chair_irc2_ab.jpg|thumb|center|300px|IRC graph2]]

From the graphs above it can be seen that the progression of the points along the IRC leads to a structure with low energy and a gradient close to zero. This relates to the local minimum and is reached by taking steps in the direction with the steepest gradient. Initially the energy drops rapidly until small changes to the structure result in slightly lower energies. The summary of the lowest energy structure can be seen below.

[[File:Summary_chair_irc_ab.JPG|thumb|center|400px|Summary for IRC]]

'''IRC opt'''

The final structure from the IRC above may not be the one with the minimum geometry therefore this molecule can then be optimised further using the three different methods explored below.

''(i) The last point of the IRC is minimised''

The last point of the IRC was taken and optimised using Hartree-Fock method with 3-21G basis set. The resulting molecule had C2 symmetry, therefore it can be related to the gauche2 structure in the reactants and products table above. The energy of this minimum is -231.69167 Hartrees, this value directly links to the appendix value (-231.69167) therefore it can be assumed that the minimum reached is of the gauche2 conformation.

[[Image:Opt_irc26_ab.JPG|thumb|center|150px|Optimised structure 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Opt_irc26_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

[[File:Summary_opt_irc26_ab.JPG|thumb|center|400px|Summary for minimised structure of IRC 26]]

A disadvantage of this method is that one can not be sure if the correct minimum has been reached. This is due to the fact that this calculation will take you to the closest minimum which may not always be the lowest minimum.

''(ii) Increasing the number of points on the IRC''

The second method of optimising involved increasing the number of points on the IRC curve. This can be done in an effort to increase the number of points thus allowing a minimum to be reached. However only 26 points were found on the output file and the same geometry of the molecule was given. The energy for this molecule can be compared to the energy of the IRC carried out initially and both give the same total energy of -231.68828 Hartrees.

[[File:Irc_chair_opt100_ab.gif|thumb|center|250px|Animation of the intermediates]]

[[File:Summary_irc100_chair_ab.JPG|thumb|centre|400px|Summary for IRC increased to 100 points]]

''(iii) Compute force constants at every step''

This method involved computing force constants at every step. This is the most reliable method that can be used, however this method may not work for larger systems as it will take a long time.

[[File:Chair_ircfc_ab.gif|thumb|center|250px|Animation of the intermediate geometries]]

[[File:Chair_ircfc1_ab.jpg|thumb|center|300px|IRC graph1]]
[[File:Chair_ircfc2_ab.jpg|thumb|center|300px|IRC graph2]]

The above graphs show the points along the energy curve until the minimum was reached. However on the graph about the gradient, a slight incline is seen at the last point. This could correlate to the fact that the physical representation of a bond is removed between the 47th and 48th point. This may lead to a slight increase in energy towards the end of the curve. The energy for this method (-231.69166 Hartrees) is roughly similar to the energy obtained in method (i) (-231.69167) which suggests that a similar minimum has been achieved whereas the IRC and method (ii) produced a different minimum.

[[File:Summary_opt_ircfc_chair_ab.JPG|thumb|centre|400px|Summary for IRC using force constants]]

=====Boat=====

A similar method was carried out on the Boat conformer in an aim to reach the local minimum. However the methods below have lead to the formation of a minimum which is not the correct minimum, the geometry reached is similar to the conformation of gauche2. If time permited, these calculations could be re-done to try and figure out why the correct minimum was not reached.

[[File:Boat_irc_ab.gif|thumb|center|250px|Animation of intermediate boat geometries]]

[[File:Boat_irc_ab.jpg|thumb|center|300px|IRC graph1]]
[[File:Boat_irc1_ab.jpg|thumb|center|300px|IRC graph2]]

[[File:Summar_boat_irc_ab.JPG|thumb|centre|400px|Summary for IRC]]

'''IRC Opt'''

''(i) The last point of the IRC is minimised''

[[Image:Boat_ircopt_ab.JPG|thumb|centre|150px|Optimised structure 
<jmol>
<jmolAppletButton>
<uploadedFileContents>B_irc_opt20_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

[[File:Summary_boat_ircopt_ab.JPG|thumb|centre|400px|Summary]]

''(ii) Increasing the number of points on the IRC''

[[File:Boat_irc100_ab.JPG|thumb|centre|200px|Structure of final point on 100 point IRC]]

[[File:Summary_boat_irc100_ab.JPG|thumb|centre|400px|Summary for IRC increased to 100 points]]

''(iii) Compute force constants at every step''

[[File:Boat_ircfc_anim_ab.gif|thumb|center|250px|Animation of the intermediate geometries]]

[[File:Boat_ircfc_graph1_ab.jpg|thumb|center|300px|IRC graph1]]
[[File:Boat_ircfc_graph2_ab.jpg|thumb|center|300px|IRC graph2]]

[[File:Summary_boat_ircfc_ab.JPG|thumb|centre|400px|Summary for IRC using force constants]]

====Activation energy====

''Compare Gauss values to the experimental values at 0K'':
The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K.

==Diels Alder Cycloaddition reaction==

The Diels Alder Cycloaddition reaction is known as a type of pericyclic reaction between a diene and a dienophile to form a cyclohexene system. The π orbitals on the dienophile form new σ bonds with the π orbital from the diene. Usually if the HOMO of one interacts with the LUMO of the other than the cycloaddition is allowed, however both molecular orbitals need to have the same symmetry otherwise there will be no overlap and therefore the reaction will not proceed.
The ''Cis principle'' <ref name=Sauer>
J. Sauer,
''Diels-Alder reactions II: The reaction mechanism'',
'''1967''',
17,
{{DOI| 10.1002/anie.196700161}} </ref> states that the stereochemistry of the reactants is maintained in the product and therefore the subsituents will be on the same face of the ring in the product. The maleic anhydride example below shows this, however the cis substituents are part of a ring and are therefore on the same face due to steric lock.

===Butadiene and Ethylene===

Butadiene and Ethylene can undergo a [4+2]- Cycloaddition to form cyclohexene. The reaction involves the interaction between the HOMO and LUMO's of Butadiene and Ethylene as seen below.

[[File:Homolumobutadiene_ab.gif|thumb|center|300px|HOMO and LUMO interactions]]

These LCAO's represent the interaction between the π and π* orbitals of the reactants. The Molecular orbitals obtained from the calculations will prove these interactions.

====Optimising butadiene====

A molecule of butadiene was drawn in GaussView and optimised using the Semi-empirical molecular orbital method with the AM1 basis set. Cis butadiene is used to ensure maximum orbital overlap is achieved.

[[Image:Butadiene_opt_am1_ab.JPG|thumb|center|150px|The structure of AM1 optimised cis-butadiene 
<jmol>
<jmolAppletButton>
<uploadedFileContents>Butadiene_opt_am1_ab.mol</uploadedFileContents>
<text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

'''HOMO- LUMO'''

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''MO'''
| align="center" style="background:#f0f0f0;"|'''Image'''
| align="center" style="background:#f0f0f0;"|'''LCAO'''
| align="center" style="background:#f0f0f0;"|'''Symmetry'''
|-
| HOMO||[[File:Homoe_butadiene_ab.jpg|150px]]||[[File:Homolcao_butadiene_ab.gif|150px]]||anti-symmetric
|-
| LUMO||[[File:Lumo_butadiene_ab.jpg|150px]]||[[File:Lumolcao_butadiene_ab.gif|150px]]||symmetric
|-
|
|}

====Transition State geometry====

The ethylene approaches the cis butadiene from above, in an aim to maximum the overlap between the π orbitals.

[[Image:42_ts_ab.JPG|thumb|center|150px|Transition structure with C-C bond lengths 
<jmol>
<jmolAppletButton>
<uploadedFileContents>42_optfreq_am1_ab.mol</uploadedFileContents>
<script> measure 5 14; measure 8 11 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

The bond lengths visible in the Jmol above shows the σ bond lengths of the partially formed C-C bonds. The typical Csp3-sp3 in cyclohexane is 1.535Å<ref name=Allen>
Frank H. Allen, Olga Kennard and David G. Watson,
''J. Chem. Soc. Perkin Trans. II'',
'''1987''',
S6-S7</ref>, and the typical Csp2-Csp2 bond length is 1.455<ref name=Allen>
Frank H. Allen, Olga Kennard and David G. Watson,
''J. Chem. Soc. Perkin Trans. II'',
'''1987''',
S6-S7</ref>. Therefore it can be seen that the partially formed σ bond is much longer than both of these lengths as it is not yet a bond, however once formed it will relate most to the Csp3-sp3 length.

The optimised transition state had an imaginary frequency at -956.14cm-1, this relates to the formation of the new σ-bonds which is synchronous.

[[File:Imaginaryfreq_ts_da_ab.gif|thumb|centre|250px|Animation of imaginary frequency]]

This can then be compared tot he frequency of the lowest positive vibration at 147.29cm-1, which shows an asynchronous movement and does not relate to the formation of the new σ bonds.

[[File:Lowestpos_ab.gif|thumb|centre|250px|Animation of lowest frequency]]

'''HOMO-LUMO'''

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [[File:Homo_ts_da_ab.jpg|thumb|center|150px|HOMO]]||[[File:Lumo_ts_da_ab.jpg|thumb|center|150px|LUMO]]
|-
| Anti-symmetric||Symmetric
|-
|
|}

The above diagrams show a molecular orbital representation of the π/ π* interaction of ethylene and the HOMO/LUMO of butadiene. The reaction is [4s + 2s] due to the fact that butadiene has 4 π orbitals in the π system and ehtylene has 2 π orbitals. The molecular orbitals of ethylene and butadiene have been labelled as symmetric and anti-symmetric with respect to the middle plane. The reason this reaction is allowed is because the HOMO of one interacts with the LUMO of the other, therefore it can be seen that the molecular orbitals of the transition state match the LCAO's predicted before the calculations were carried out.

===Cyclohexa-1,3-diene reaction with Maleic Anhydride===

This exercise aims to prove the fact that the cycloaddition reaction between cyclohexa-1,3-diene and maleic anhydride results in the primarily formation of the endo structure. This is due to the fact that the endo structure is lower in energy therefore the reaction is kinetically controlled resulting in a regioselective reaction.

[[File:Exoendoma_ab.gif|thumb|center|500px|Reaction of cyclohexa-1,3-diene and maleic anhydride to form the exo and endo adducts]]

====Exo Tranition structure====

The exo and endo structures were calculated using the freeze coordination method. The cyclohexa-1,3-diene were optimised separately and then a guess structure of the transition state was made. The distance between the two carbons forming the new bonds were frozen at 2.2Å and then optimised using HF/3-21G. This step allows the rest of the atoms to relax whilst freezing the reacting carbons in their place.

The output file of this structure was optimised further by using derivate bonds, thus allowing them to move to form the optimum transition structure:

[[Image:P3_exo_ab.JPG|thumb|center|150px|Exo transition state 
<jmol>
<jmolAppletButton>
<uploadedFileContents>P3_exo_ab.mol</uploadedFileContents>
<script> measure 1 16; measure 4 17 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

This structure also displayed an imaginary frequency at -647.42cm-1 with an intensity of 67.5. From the animation below it can be seen that this vibration links directly to the formation of the new σ-bonds.

[[File:Ma_im_exo_ab.gif|thumb|centre|250px|Animation of imaginary frequency]]

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [[File:Homo_exo1_ma_ab.jpg|thumb|center|150px|Homo for the exo structure]]||[[File:Lumo_exo1_ma_ab.jpg|thumb|center|150px|Lumo for the exo structure]]
|-
|
|}

====Endo Transition structure====

[[Image:P3_endo_ab.JPG|thumb|center|150px|Endo transition state 
<jmol>
<jmolAppletButton>
<uploadedFileContents>P3_endo_ab.mol</uploadedFileContents>
<script> measure 1 17; measure 4 16 </script><text>Click here for Jmol</text>
</jmolAppletButton>
</jmol>]] 

{| class=wikitable
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [[File:Homo_endo_ma_ab.jpg|thumb|center|200px|Homo for the endo structure]]||[[File:Lumo_endo_ma_ab.jpg|thumb|center|200px|Lumo for the endo structure]]
|-
|
|}

====Comparison between endo and exo transition states====

{| {{table}} | align="center" style="background:#f0f0f0;"|'''''' | align="center" style="background:#f0f0f0;"|'''exo''' | align="center" style="background:#f0f0f0;"|'''endo''' |- | Method||HF/3-21G||HF/3-21G |- | Energy (Hartrees)||-605.60352||-605.61037 |- | |}

From the above table it can be seen that the endo structure is more stable

Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

==References==
<references/>