File:Cope.jpg

2015-11-05T23:37:12Z

Svp13: Svp13 uploaded a new version of File:Cope.jpg

Rep:Mod:svp

2015-11-05T21:15:22Z

Svp13: /* AM1 Semi-empirical Molecular Orbital Method */

==Introduction==
The aim of this experiment was to characterise transition states for the Diels Alder cycloaddition and Cope rearrangement, computationally using the GaussView program. By doing so transition structures and the preferred reaction mechanism could be elucidated for the Cope rearrangement.

== The Cope Rearrangement Tutorial ==

The following tutorial explored the reactivity of 1,5-hexadiene in the Cope rearrangement. The mechanism by which the diene rearranges has previously been a topic of debate, owing to many computational and experimental studies. 1,5-hexadiene undergoes a pericyclic [3,3]-sigmatropic shift in a concerted fashion. The diene passes through either a chair or boat transition structure, the latter lying several kcal mol-1 higher in energy [2]. Previously computational studies have been ambiguous, making an agreement upon the mechanism difficult due to the flatness of potential energy surfaces belonging to the boat and chair transition states [3].In the following experiment activation energies were calculated by comparing the energies computed at the B3LYP/6-31G* level of theory, using the more sophisticated density functional theory (DFT) method. This method/basis set produces energies that comply with experimental data.

EXPERIMENT PICTURE -

=== Optimising the Reactants ===

==== “Anti2” conformation of 1,5- hexadiene ====
In Gaussview an “anti2” 1, 5- hexadiene molecule was built in an anti-peri-planar conformation. The molecule was cleaned before an optimisation was run at the Hartree Fock, 3-21G level of theory. This optimisation is run often as a pre-requisite to the more computationally expensive DFT (6-31G*) method. Cleaning before optimisation adjusts the geometry of the molecule in accordance with a set of parameters designed to produce a molecule that would be expected chemically.
Once optimised and all the calculations had converged, the structure was symmetrised and the point group was found to be Ci, on the highest tolerance setting. The energy of the molecule was found to be -231.69 a.u; this is in accordance with the energy provided in lab script appendix.
{| class="wikitable"
!Structure
!Point group
!Energy/ Hartrees
HF/3-21G
|-
|[[File:Anti structure.jpg|none|x200px]]
|Ci
|<nowiki>-231.69253522</nowiki>
|}

==== “Guache3” conformation of 1,5- hexadiene ====

Similarly to the anti-conformation the “gauche3” conformation was built and optimised at the Hartree Fock, 3-21G level of theory. The resultant energy was found to be less than the anti conformation and the given point group was C1 after symmetrising the molecule. The energy was again in agreement with the lab script value.

(Picture and table)

When calculating activation energies the lowest energy conformer of the reactant is used as a starting point. Chemical intuition would indicate that the “anti 2” conformation of 1,5- hexadiene would be the lowest in energy, due to steric effects. Studies such and including this have found the “guache 3” conformation to be the lowest. It has been suggested that this is due to an interaction between the vinyl proton and the c-c π electrons; such a bonding interaction accounts for the extra stability of the guache conformation. This effect is termed as the “CH-π” interaction (source).
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
HF/3-21G
|-
|<gallery>
File:Gauche 3.jpg
</gallery>
|C1
|<nowiki>-231.69266122</nowiki>
|}

=== DFT Optimisation of Reactants ===

The "Anti 2" 1,5- hexadiene molecule was re-optimised using the B3LYP/6-31G(d) level of theory using the DFT method. This is a higher level of theory than the Hartree fock 3-21G method; which is often done as a prerequisite to reduce the computational expense associated with the higher level of theory. After the second optimisation the point group of the molecule remained Ci. The energy was found to be -234. 61 a.u. in agreement with the value provided in the lab script appendix.

In order for the computed energies of the hexadiene molecules to be comparable with experimental data, a frequency calculation must be completed. After-which it is then possible to identify the critical point (a point at which all vibrational frequencies are real and positive). A frequency calculation was conducted on the 6-31G(d) optimised anti- hexadiene at the same level of theory. Once run, the vibrational frequencies of the molecule were checked to be all positive and real, and the infrared spectrum was generated.

A note of the following energies were taken from the the output file:
* The sum of electronic and zero-point energies (-234.416255 a.u.)
* The sum of electronic and thermal energies (-234.408963 a.u.)
* The sum of electronic and thermal enthalpies (-234.408019 a.u.)
* The sum of electronic and thermal free energies (-234.447872 a.u.)
The sum of electronic and zero point energies is similar to the experimental value, conducted at 0 K.
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
DFT/631G(d)
!IR spectrum
|-
|
[[File:Anti structure.jpg|x200px]]

|Ci
|<nowiki>-234.61171166</nowiki>
|
[[File:IR anti.jpg|x250px]]

|}

=== Optimizing the "Chair" and "Boat" Transition States ===

==== The Chair ====
In the following section the transition structures were built and optimised using a variety of methods:

(i)Computing the force constants at the start of the calculation.

(ii)Using the redundant coordinate editor.

(iii)Using the QST2 method.

Following optimization the intrinsic reaction coordinate (IRC) was run. This allows a path of minimum energy to be followed from a transition state structure down to the local minimum of the potential energy surface.

The chair transition state was composed of 2 allyl fragments, that were first optimized individually using the HF/3-21G level of theory before making each transition state in GaussView. The terminal carbon atoms of the allyl fragments were set to be 2.2 Å apart and were arranged into a chair like orientation. This guess transition state was then optimized using 2 different methods, both of which using Hartree Fock and the 3-21G basis set. It is necessary to use alternative methods to a typical minimization when optimizing a transition state as the program needs to be aware of the direction of negative curvature. '''(MORE DETAIL)'''

(i)The first method used was the TS (Berny) method; when optimizing using this method a good knowledge of the transition structure geometry is required. If the geometry is far from the true transition state geometry the optimization fails. The force constants in the this case were calculated once.

After the optimization had completed, one imaginary frequency at -818.81 cm-1 was found, indicating a transition structure had been reached. An imaginary frequency is produced at a transition state as a result of the resultant force constant being negative. As the frequency of motion is proportional to the square root of the force constant, an imaginary number is produced as a result.
{| class="wikitable"
!Transition State
!Structure
!Energy/ Hartrees
TS(Berny)
!Point Group
|-
|[[File:TS Frequency Chair.gif]]
|
[[File:Chair TS.jpg|x250px]]
|<nowiki>-231.6172118</nowiki>
|C2h
|}

(ii) The frozen coordinate method was then used, it can be used before running a TS (Berny) calculation. This is a suitable choice when the predicted transition state structure is not close to the real structure. The redundant coordinator editor was used to freeze the terminal c-c bond distances to 2.2 Å for the first optimization. Once the rest of the molecule had been optimized to a minimum the distances were "unfrozen" and a TS (Berny) calculation was run in a similar fashion as above except the force constants in this case were not calculated.
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
Frozen Coordinate
!Transition State
(Animation)
|-
|
[[File:TS Froze Chair.jpg|x250px]]
|C2h
|<nowiki>-231.61521115</nowiki>
|[[File:Chair Froze TS.gif]]
|}
Comparatively the two methods provide very similar results. The first although being quicker and less computationally expensive however would not suffice in situations where the transition state geometry deviated far from reality. The geometry of the two transition states was similar, with both belonging to the C2h point group. The bond forming/bond breaking lengths were 2.02047 Å after optimizing using the TS (Berny) alone and slightly longer after using the frozen coordinate method at 2.19939 Å.

==== The Boat ====
(iii) The boat transition structure was then optimized using the QST2 method.''' (MORE DETAIL)''' This method locates the transition structure based on the reactants and products. Such a method can be useful if the structure of the transition state is not known precisely.

Two of the previously optimized "Anti2", Ci 1,5- hexadiene molecules were arranged and numbered in a specific order, as shown below. As can be seen the optimization failed, the structure produced was highly dissociated and clearly does not show the expected boat transition structure.

{| class="wikitable"
!Starting Structure
!Structure after Optimization
|-
|
[[File:QST2 Numbered inc.jpg|x200px]]
|
[[File:QST2 Wrong TS.jpg|x200px]]

|}
The optimization above failed ad the QST2 method requires that the reactants and products be in a geometry close enough to the transition state.

A second optimization was then run, this time the dihedral angle was changed to 0° and the molecule was manipulated until molecules had geometry below was reached. The optimization was run again. It converged to the transition structure and one imaginary frequency (-839.86) was produced.
{| class="wikitable"
!Starting Structure
!Transition Structure
!Point group
!Energy/ Hartrees
QST2
!Transition State
(Animation)
|-
|
[[File:QST2 Starting.jpg|x250px]]
|
[[File:QST2 Boat TS.jpg|x250px]]
|C2V
|<nowiki>-231.60280239</nowiki>
|[[File:Boat TS QST2.gif]]
|
|}
It is not possible at this stage to decipher which of the conformers of 1,5- hexadiene corresponds to which transition state. It it however possible using and IRC to follow the minimum energy path of a transition structure down to its local minimum. It does so by travelling along the steepest part of the potential energy surface.

==== IRC Calculation ====
Next an IRC was conducted on the chair transition state structure previously optimized using the frozen coordinate method. The number of steps within an IRC calculation may be set; in this case an IRC was run in the forward direction due to the symmetrical nature of the reaction coordinate. The number of steps was set to 50.

{| class="wikitable"
!IRC plot
!Final Geometry after IRC Calculation
|-
|
[[File:IRC Chair plot.png|x250px]]
|
[[File:Step 50 IRC chair.jpg|x250px]]
|}
It can be seen from the plot that once the calculation had finished the structure had not reached a minimum geometry. From the IRC you can see the energy plateau, however it had not reached a minimum. This suggests there were too few steps run, it can however be difficult to know the correct number of steps to use, as if too many are used the coordinate may veer off and an alternative energy path may be followed. In order to obtain the minimum a normal minimization was run using Hartree Fock and the 3-21G basis set. The final structure was that of the chair transition state, and the energy was found to be -231.692239 a.u. This is similar to both of the "gauche2" and "gauche3" conformers of 1,5 -hexadiene energies, visually it could be seen to resemble the "gauche3" conformer, belonging to the C1 point group.

==== Activation Energies ====
Lastly the activation energies for the reaction via both transition sates were calculated. Both transition structure were re-optimized using the DFT/ B3LYP/6-31G(d) level of theory. Frequency calculations were conducted on the structures previously optimized at the Hartree Fock 3-21G level.
{| class="wikitable"
!Structure
!Energy 3-21G/
Hartrees
!Energy 6-31G(d)/
Hartrees
!Energy + Zero Point
Energy 3-21G/

Hartrees (at 0 K)
!'''Sum of Electronic '''and Thermal Energies 3-21G

(at 298.15 K)
!Energy + Zero Point
Energy 6-31G(d)/

Hartrees (at 0 K)
!'''Sum of Electronic'''and Thermal Energies 6-31G(d)

(at 298.15 K)
!Point Group
3-21G , 631G(d)
|-
|"Anti2" conformer
|<nowiki>-231.69253522</nowiki>
|<nowiki>-234.61171166</nowiki>
|<nowiki>-231.539611</nowiki>
|<nowiki>-231.532567</nowiki>
|<nowiki>-234.468755</nowiki>
|<nowiki>-234.461963</nowiki>
|Ci , Ci
|-
|Boat TS
|<nowiki>-231.60280239</nowiki>
|<nowiki>-234.54307876</nowiki>
|<nowiki>-231.450924</nowiki>
|<nowiki>-231.445294</nowiki>
|<nowiki>-234.402360</nowiki>
|<nowiki>-234.396016</nowiki>
|C2v , C2v
|-
|Chair TS
|<nowiki>-231.61721180</nowiki>
|<nowiki>-234.55692628</nowiki>
|<nowiki>-231.466701</nowiki>
|<nowiki>-231.461341</nowiki>
|<nowiki>-234.416255</nowiki>
|<nowiki>-234.408999</nowiki>
|C2v , C2v
|}
The activation energies were calculated by finding the difference between the reactant energy and the transition state energy, these are shown below in Kcal mol-1.
{| class="wikitable"
!
!HF/ 3-21G
at 0 K
!B3LYP/ 6-31G(d)
at 0 K
!HF/ 3-21G
at 298.15 K
!B3LYP/ 6-31G(d)
at 298.15 K
!Experiment / Kcal mol-1at 0 K
|-
|ΔE '''(Chair)''' / Kcal mol-1
|45.75
|32.57
|44.72
|33.24
|33.5 ± 0.5
|-
|ΔE '''(Boat)''' / Kcal mol-1
|55.65
|41.66
|54.84
|41.38
|44.7 ± 2.0
|}
Overall the results match the expected computed values reasonably well. It can be seen that the geometry remains similar for both basis sets; whilst the energies differ considerably. It is clear that either basis set is an adequate tool for examining the geometry of molecules however when comparing energies the higher level of theory proves to be more accurate. For both levels of theory however there appears to be a general overestimation of the activation energy when computing them with GuassView as opposed to obtaining them experimentally. This overestimation reflects the approximations the program makes. In particular the computation of just one molecule introduces error, as inter-molecular forces are not taken into account. There are also calculations that may be run at a higher level of theory that would improve the accuracy of the results.

== The Diels-Alder Cycloaddition ==
The following part of the experiment explored the Diels-Alder cycloaddition by investigating the transition state structures and analyzing molecular orbitals. The Diels-Alder cycloaddition is [4+2] pericyclic addition, in which two conjugated π systems add to form a ring. This occurs in a concerted fashion via a cyclic transition state. Heat is not necessarily required to drive the reaction as the formation of two new sigma bonds over the loss of two π bonds is favored, however heat is often use to drive the reaction. The prototypical example of ethene (the dienophile) and cis-butadiene (the diene) is shown below.

[[File:DA.jpg|x200px]]

Diels-Alder cycloadditons may be termed normal electron demand additions, in which the diene is electron rich and the dienophile is electron deficient; or as inverse electron demand additions if reverse is the case. The electronic properties dictate the interactions between the HOMO's and LUMO's of a given reaction. For an allowed reaction the HOMO of one of the reactants must interact with the LUMO of the other. In more complex cases in which the reactants carry substituents, secondary orbital effects are possible. These topics were explored during the experiment.

=== Prototypical Reaction ===

Firstly the HOMO and LUMO of cis-butadiene was visualized after optimization using the AM1 semi-empirical molecular orbital method. The HOMO is anti-symmetric with respect to the plane of symmetry through the molecule, and the LUMO is anti-symmetric.

{| class="wikitable"
!Cis-butadiene LUMO
!Cis-butadiene HOMO
|-
|
[[File:Butadiene LUMO.jpg|x250px]]

|
[[File:HOMO Butadiene.jpg|x250px]]
|}

Next an approximate transition structure was built using the optimized cis-butadiene and and optimized ethene molecule. The transition state structure was drawn so as to maximize the orbital overlap between the HOMO of cis-butadiene and the LUMO of ethene. The inter-fragment distances were set to be 2.2 Å and the point group to Cs. The structure was then optimized using the TS (Berny) method and the 3-21G basis set. This method was selected as for the prototypical reaction it was not necessary to use the freeze coordinate method, since the transition state geometry was a reasonably close guess. The calculation completed producing one imaginary frequency was obtained at -818.31 cm-1, indicating a transition state was reached. The point group was Cs. Afterwards an IRC calculation was also run in both directions, the plot is shown below.
{| class="wikitable"
!Structure
!IRC Plot
!Transition Structure
|-
|
[[File:But TS.jpg|x270px]]

|
[[File:IRC butadiene.jpg|x250px]]
|[[File:Butadiene TS.gif]]
|}
The imaginary frequency representing the transition state, shown above, indicates that the reaction proceeds in a concerted fashion, where the bonds are made and broken synchronously.The partly formed c-c bond lengths were 2.20940 Å and 2.20975, indicating that the transition state partial bonds are slightly longer than the approximate 2.2 Å used to build the transition state. '''TYPICAL SP3 BOND lengths etc discussion '''

<nowiki> </nowiki>The lowest positive frequency is shown below. Conversely here bond formation is happening in an asynchronous fashion.

[[File:Lowest pos frequ.gif]]

The HOMO and LUMO of the transition structure was then evaluated. The symmetrical LUMO and the anti-symmetrical HOMO are shown below.
{| class="wikitable"
!Anti-symmetrical HOMO
!Symmetrical LUMO
|-
|
[[File:AS HOMO CYCLOHEX.jpg|x270px]]

|
[[File:SYM LUMO CYCLOHEX.jpg|x270px]]

|}
It can be seen that the LUMO of the electron deficient ethene interacts with the HOMO of the butadiene to form the the HOMO above. This is the case for normal electron demand additions; as the energy gap between the LUMO of the diene and the HOMO of the dienophile is smaller than the converse gap between the LUMO of the dieneophile and the HOMO of the diene.

==== Maleic anhydride and Cyclohexa-1,3-diene Diels-Alder ====
The selectivity of the Diels-Alder reaction was then studied by evaluating the 2 possible transition states (endo and exo) that are possible in the reaction between maleic anhydride and cyclohexa-1,3-diene. The kinetically controlled reaction proceeds primarily via the endo transition state to give the kinetically favored endo product (also referred to as the endo rule). The two products can be seen below.

[[File:ENDO EXO Prods.jpg|x200px]]

Firstly maleic anhydride and a cyclohexa-1,3-diene molecules were optimized individually before making the transition structures. The endo guess transition structure was built first in GaussView, so that the π orbitals belonging to the carbonyl groups of the maleic anhydride were lying underneath the π orbitals of the cyclohexa-1,3-diene. The partial bonds between two fragments were set to be 2.2 Å again and the point group to Cs. Secondly optimizations were run, using two different basis sets for comparison: The Hartree Fock/ 3-21G level of theory and the AM1 semi-empirical molecular orbital method. In both cases an initial optimization was run using the frozen coordinate method, as it was likely that the transition structures were too dissimilar from reality to run a TS (Berny) calculation first. For both transition structures the partial c-c sp3 bond lengths were frozen to 2.2 Å and optimized, the bonds were then "unfrozen" as before and re-optimized using the TS (Berny) method. The point group remained Cs. One imaginary frequency was found at -605.60 cm-1; the corresponding frequency is shown below.

===== Hartree Fock Method =====
{| class="wikitable"
!Endo Structure
!Transition State
!Energy/ Hartrees
HF/3-21G
!HOMO
!LUMO
|-
|
[[File:ENDO TS.jpg|x250px]]

|
[[File:ENDO HF BERNY.gif]]

|<nowiki>-605.64958804</nowiki>
|
[[File:ENDO TS HOMO.jpg|x250px]]

|
[[File:Endo LUMO HF.jpg|x250px]]

|}

It can be seen that the LUMO is symmetrical with respect to the plane of symmetry, and the HOMO is anti-symmetrical.

Secondary orbital interactions.

The transition state animation shows the synchronicity of the bond formation.

Next the exo transition structure was made, this time ensuring the that the carbonyl groups of the anyhydride were pointing away from the the diene π bonds. The treatment was applied as above. Again the point group was Cs and an imaginary frequency was found at -647.53 cm-1.
{| class="wikitable"
!Exo Structure
!Transition State
!Energy/ Hartrees
HF/3-21G
!HOMO
!LUMO
|-
|
[[File:EXO TS Berny.jpg|x250px]]

|
[[File:EXO BERNY TS Freq.gif]]

|<nowiki>-605.60359125</nowiki>
|
[[File:EXO HOMO berny.jpg|x250px]]

|
[[File:EXO LUMO Berny.jpg|x250px]]

|}
Similarly here the bond forming is synchronous and facile. Both the HOMO and LUMO are anti-symmetrical with respect to the plane.

'''MORE DETAIL ON BONDING '''

===== AM1 Semi-empirical Molecular Orbital Method =====
The same process as above was followed, however this time using the semi-empirical method. The results are summarized below. Imaginary frequencies were found for the endo and exo transition states, they were ..... and -810.88 cm-1 respectively. The point groups for both were as before Cs.

{| class="wikitable"
!Structure
!Transition State
!Energy / Hartrees
Semi-empirical AM1
!HOMO
!LUMO
|-
|
|
|
|
|
|-
|EXO
[[File:AM1 EXO TS.jpg|x250px]]

|
[[File:EXO AM1 TS Vib.gif]]

|<nowiki>-0.05042001</nowiki>
|
[[File:EXO AM1 Berny HOMO.jpg|x250px]]

|
[[File:LUMO EXO AM1.jpg|x250px]]

|-
|ENDO
[[File:AM1 ENDO TS IMAGE.jpg|x250px]]

|
[[File:ENDO AM1 TS vib.gif]]

|<nowiki>-0.05119821</nowiki>
|
[[File:ENDO HOMO AM1.jpg|x250px]]

|
[[File:AM1 LUMO ENDO.jpg|x250px]]

|}
By comparison of the two methods it is again clear that using different methods does not have a great effect on the outcome of the geometry, but does however with regards to the energy.

A sketch was produced of both transition structures, and the bond lengths compared. By looking at the extent of bonding in each is is possible to evaluate the interactions between the molecules further.
{| class="wikitable"
!Exo sketch
!C10-C2 / Å
!C14 -15 / Å
!C10-C15 / Å
!C13-C14 / Å
|-
|
[[File:Numbered EXO TS 1.jpg|x250px]]

|2.26065
|1.39758
|1.37003
|1.37003
|}
{| class="wikitable"
!Endo sketch
!C4 - C16/ Å
!C4 - C5 / Å
!C5-C6/ Å
!C6-C1 / Å
|-
|
[[File:Numbered ENDO TS 1.jpg|x250px]]

|2.17057
|1.39436
|1.39679
|1.39436
|}
The majority of bond length in the table are in between that of a single sp3–sp3 c-c bond length (1.52 Å) and the sp3–sp2 c-c bond length (~134 Å for multiple bonds), these bond lengths correspond to the double bonds that are either being broken or formed during the reaction. The endo transition state is the more stable, as a result of this there is more bonding character between the two fragments.

Rep:Mod:svp

2015-11-05T21:08:31Z

Svp13: /* AM1 Semi-empirical Molecular Orbital Method */

==Introduction==
The aim of this experiment was to characterise transition states for the Diels Alder cycloaddition and Cope rearrangement, computationally using the GaussView program. By doing so transition structures and the preferred reaction mechanism could be elucidated for the Cope rearrangement.

== The Cope Rearrangement Tutorial ==

The following tutorial explored the reactivity of 1,5-hexadiene in the Cope rearrangement. The mechanism by which the diene rearranges has previously been a topic of debate, owing to many computational and experimental studies. 1,5-hexadiene undergoes a pericyclic [3,3]-sigmatropic shift in a concerted fashion. The diene passes through either a chair or boat transition structure, the latter lying several kcal mol-1 higher in energy [2]. Previously computational studies have been ambiguous, making an agreement upon the mechanism difficult due to the flatness of potential energy surfaces belonging to the boat and chair transition states [3].In the following experiment activation energies were calculated by comparing the energies computed at the B3LYP/6-31G* level of theory, using the more sophisticated density functional theory (DFT) method. This method/basis set produces energies that comply with experimental data.

EXPERIMENT PICTURE -

=== Optimising the Reactants ===

==== “Anti2” conformation of 1,5- hexadiene ====
In Gaussview an “anti2” 1, 5- hexadiene molecule was built in an anti-peri-planar conformation. The molecule was cleaned before an optimisation was run at the Hartree Fock, 3-21G level of theory. This optimisation is run often as a pre-requisite to the more computationally expensive DFT (6-31G*) method. Cleaning before optimisation adjusts the geometry of the molecule in accordance with a set of parameters designed to produce a molecule that would be expected chemically.
Once optimised and all the calculations had converged, the structure was symmetrised and the point group was found to be Ci, on the highest tolerance setting. The energy of the molecule was found to be -231.69 a.u; this is in accordance with the energy provided in lab script appendix.
{| class="wikitable"
!Structure
!Point group
!Energy/ Hartrees
HF/3-21G
|-
|[[File:Anti structure.jpg|none|x200px]]
|Ci
|<nowiki>-231.69253522</nowiki>
|}

==== “Guache3” conformation of 1,5- hexadiene ====

Similarly to the anti-conformation the “gauche3” conformation was built and optimised at the Hartree Fock, 3-21G level of theory. The resultant energy was found to be less than the anti conformation and the given point group was C1 after symmetrising the molecule. The energy was again in agreement with the lab script value.

(Picture and table)

When calculating activation energies the lowest energy conformer of the reactant is used as a starting point. Chemical intuition would indicate that the “anti 2” conformation of 1,5- hexadiene would be the lowest in energy, due to steric effects. Studies such and including this have found the “guache 3” conformation to be the lowest. It has been suggested that this is due to an interaction between the vinyl proton and the c-c π electrons; such a bonding interaction accounts for the extra stability of the guache conformation. This effect is termed as the “CH-π” interaction (source).
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
HF/3-21G
|-
|<gallery>
File:Gauche 3.jpg
</gallery>
|C1
|<nowiki>-231.69266122</nowiki>
|}

=== DFT Optimisation of Reactants ===

The "Anti 2" 1,5- hexadiene molecule was re-optimised using the B3LYP/6-31G(d) level of theory using the DFT method. This is a higher level of theory than the Hartree fock 3-21G method; which is often done as a prerequisite to reduce the computational expense associated with the higher level of theory. After the second optimisation the point group of the molecule remained Ci. The energy was found to be -234. 61 a.u. in agreement with the value provided in the lab script appendix.

In order for the computed energies of the hexadiene molecules to be comparable with experimental data, a frequency calculation must be completed. After-which it is then possible to identify the critical point (a point at which all vibrational frequencies are real and positive). A frequency calculation was conducted on the 6-31G(d) optimised anti- hexadiene at the same level of theory. Once run, the vibrational frequencies of the molecule were checked to be all positive and real, and the infrared spectrum was generated.

A note of the following energies were taken from the the output file:
* The sum of electronic and zero-point energies (-234.416255 a.u.)
* The sum of electronic and thermal energies (-234.408963 a.u.)
* The sum of electronic and thermal enthalpies (-234.408019 a.u.)
* The sum of electronic and thermal free energies (-234.447872 a.u.)
The sum of electronic and zero point energies is similar to the experimental value, conducted at 0 K.
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
DFT/631G(d)
!IR spectrum
|-
|
[[File:Anti structure.jpg|x200px]]

|Ci
|<nowiki>-234.61171166</nowiki>
|
[[File:IR anti.jpg|x250px]]

|}

=== Optimizing the "Chair" and "Boat" Transition States ===

==== The Chair ====
In the following section the transition structures were built and optimised using a variety of methods:

(i)Computing the force constants at the start of the calculation.

(ii)Using the redundant coordinate editor.

(iii)Using the QST2 method.

Following optimization the intrinsic reaction coordinate (IRC) was run. This allows a path of minimum energy to be followed from a transition state structure down to the local minimum of the potential energy surface.

The chair transition state was composed of 2 allyl fragments, that were first optimized individually using the HF/3-21G level of theory before making each transition state in GaussView. The terminal carbon atoms of the allyl fragments were set to be 2.2 Å apart and were arranged into a chair like orientation. This guess transition state was then optimized using 2 different methods, both of which using Hartree Fock and the 3-21G basis set. It is necessary to use alternative methods to a typical minimization when optimizing a transition state as the program needs to be aware of the direction of negative curvature. '''(MORE DETAIL)'''

(i)The first method used was the TS (Berny) method; when optimizing using this method a good knowledge of the transition structure geometry is required. If the geometry is far from the true transition state geometry the optimization fails. The force constants in the this case were calculated once.

After the optimization had completed, one imaginary frequency at -818.81 cm-1 was found, indicating a transition structure had been reached. An imaginary frequency is produced at a transition state as a result of the resultant force constant being negative. As the frequency of motion is proportional to the square root of the force constant, an imaginary number is produced as a result.
{| class="wikitable"
!Transition State
!Structure
!Energy/ Hartrees
TS(Berny)
!Point Group
|-
|[[File:TS Frequency Chair.gif]]
|
[[File:Chair TS.jpg|x250px]]
|<nowiki>-231.6172118</nowiki>
|C2h
|}

(ii) The frozen coordinate method was then used, it can be used before running a TS (Berny) calculation. This is a suitable choice when the predicted transition state structure is not close to the real structure. The redundant coordinator editor was used to freeze the terminal c-c bond distances to 2.2 Å for the first optimization. Once the rest of the molecule had been optimized to a minimum the distances were "unfrozen" and a TS (Berny) calculation was run in a similar fashion as above except the force constants in this case were not calculated.
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
Frozen Coordinate
!Transition State
(Animation)
|-
|
[[File:TS Froze Chair.jpg|x250px]]
|C2h
|<nowiki>-231.61521115</nowiki>
|[[File:Chair Froze TS.gif]]
|}
Comparatively the two methods provide very similar results. The first although being quicker and less computationally expensive however would not suffice in situations where the transition state geometry deviated far from reality. The geometry of the two transition states was similar, with both belonging to the C2h point group. The bond forming/bond breaking lengths were 2.02047 Å after optimizing using the TS (Berny) alone and slightly longer after using the frozen coordinate method at 2.19939 Å.

==== The Boat ====
(iii) The boat transition structure was then optimized using the QST2 method.''' (MORE DETAIL)''' This method locates the transition structure based on the reactants and products. Such a method can be useful if the structure of the transition state is not known precisely.

Two of the previously optimized "Anti2", Ci 1,5- hexadiene molecules were arranged and numbered in a specific order, as shown below. As can be seen the optimization failed, the structure produced was highly dissociated and clearly does not show the expected boat transition structure.

{| class="wikitable"
!Starting Structure
!Structure after Optimization
|-
|
[[File:QST2 Numbered inc.jpg|x200px]]
|
[[File:QST2 Wrong TS.jpg|x200px]]

|}
The optimization above failed ad the QST2 method requires that the reactants and products be in a geometry close enough to the transition state.

A second optimization was then run, this time the dihedral angle was changed to 0° and the molecule was manipulated until molecules had geometry below was reached. The optimization was run again. It converged to the transition structure and one imaginary frequency (-839.86) was produced.
{| class="wikitable"
!Starting Structure
!Transition Structure
!Point group
!Energy/ Hartrees
QST2
!Transition State
(Animation)
|-
|
[[File:QST2 Starting.jpg|x250px]]
|
[[File:QST2 Boat TS.jpg|x250px]]
|C2V
|<nowiki>-231.60280239</nowiki>
|[[File:Boat TS QST2.gif]]
|
|}
It is not possible at this stage to decipher which of the conformers of 1,5- hexadiene corresponds to which transition state. It it however possible using and IRC to follow the minimum energy path of a transition structure down to its local minimum. It does so by travelling along the steepest part of the potential energy surface.

==== IRC Calculation ====
Next an IRC was conducted on the chair transition state structure previously optimized using the frozen coordinate method. The number of steps within an IRC calculation may be set; in this case an IRC was run in the forward direction due to the symmetrical nature of the reaction coordinate. The number of steps was set to 50.

{| class="wikitable"
!IRC plot
!Final Geometry after IRC Calculation
|-
|
[[File:IRC Chair plot.png|x250px]]
|
[[File:Step 50 IRC chair.jpg|x250px]]
|}
It can be seen from the plot that once the calculation had finished the structure had not reached a minimum geometry. From the IRC you can see the energy plateau, however it had not reached a minimum. This suggests there were too few steps run, it can however be difficult to know the correct number of steps to use, as if too many are used the coordinate may veer off and an alternative energy path may be followed. In order to obtain the minimum a normal minimization was run using Hartree Fock and the 3-21G basis set. The final structure was that of the chair transition state, and the energy was found to be -231.692239 a.u. This is similar to both of the "gauche2" and "gauche3" conformers of 1,5 -hexadiene energies, visually it could be seen to resemble the "gauche3" conformer, belonging to the C1 point group.

==== Activation Energies ====
Lastly the activation energies for the reaction via both transition sates were calculated. Both transition structure were re-optimized using the DFT/ B3LYP/6-31G(d) level of theory. Frequency calculations were conducted on the structures previously optimized at the Hartree Fock 3-21G level.
{| class="wikitable"
!Structure
!Energy 3-21G/
Hartrees
!Energy 6-31G(d)/
Hartrees
!Energy + Zero Point
Energy 3-21G/

Hartrees (at 0 K)
!'''Sum of Electronic '''and Thermal Energies 3-21G

(at 298.15 K)
!Energy + Zero Point
Energy 6-31G(d)/

Hartrees (at 0 K)
!'''Sum of Electronic'''and Thermal Energies 6-31G(d)

(at 298.15 K)
!Point Group
3-21G , 631G(d)
|-
|"Anti2" conformer
|<nowiki>-231.69253522</nowiki>
|<nowiki>-234.61171166</nowiki>
|<nowiki>-231.539611</nowiki>
|<nowiki>-231.532567</nowiki>
|<nowiki>-234.468755</nowiki>
|<nowiki>-234.461963</nowiki>
|Ci , Ci
|-
|Boat TS
|<nowiki>-231.60280239</nowiki>
|<nowiki>-234.54307876</nowiki>
|<nowiki>-231.450924</nowiki>
|<nowiki>-231.445294</nowiki>
|<nowiki>-234.402360</nowiki>
|<nowiki>-234.396016</nowiki>
|C2v , C2v
|-
|Chair TS
|<nowiki>-231.61721180</nowiki>
|<nowiki>-234.55692628</nowiki>
|<nowiki>-231.466701</nowiki>
|<nowiki>-231.461341</nowiki>
|<nowiki>-234.416255</nowiki>
|<nowiki>-234.408999</nowiki>
|C2v , C2v
|}
The activation energies were calculated by finding the difference between the reactant energy and the transition state energy, these are shown below in Kcal mol-1.
{| class="wikitable"
!
!HF/ 3-21G
at 0 K
!B3LYP/ 6-31G(d)
at 0 K
!HF/ 3-21G
at 298.15 K
!B3LYP/ 6-31G(d)
at 298.15 K
!Experiment / Kcal mol-1at 0 K
|-
|ΔE '''(Chair)''' / Kcal mol-1
|45.75
|32.57
|44.72
|33.24
|33.5 ± 0.5
|-
|ΔE '''(Boat)''' / Kcal mol-1
|55.65
|41.66
|54.84
|41.38
|44.7 ± 2.0
|}
Overall the results match the expected computed values reasonably well. It can be seen that the geometry remains similar for both basis sets; whilst the energies differ considerably. It is clear that either basis set is an adequate tool for examining the geometry of molecules however when comparing energies the higher level of theory proves to be more accurate. For both levels of theory however there appears to be a general overestimation of the activation energy when computing them with GuassView as opposed to obtaining them experimentally. This overestimation reflects the approximations the program makes. In particular the computation of just one molecule introduces error, as inter-molecular forces are not taken into account. There are also calculations that may be run at a higher level of theory that would improve the accuracy of the results.

== The Diels-Alder Cycloaddition ==
The following part of the experiment explored the Diels-Alder cycloaddition by investigating the transition state structures and analyzing molecular orbitals. The Diels-Alder cycloaddition is [4+2] pericyclic addition, in which two conjugated π systems add to form a ring. This occurs in a concerted fashion via a cyclic transition state. Heat is not necessarily required to drive the reaction as the formation of two new sigma bonds over the loss of two π bonds is favored, however heat is often use to drive the reaction. The prototypical example of ethene (the dienophile) and cis-butadiene (the diene) is shown below.

[[File:DA.jpg|x200px]]

Diels-Alder cycloadditons may be termed normal electron demand additions, in which the diene is electron rich and the dienophile is electron deficient; or as inverse electron demand additions if reverse is the case. The electronic properties dictate the interactions between the HOMO's and LUMO's of a given reaction. For an allowed reaction the HOMO of one of the reactants must interact with the LUMO of the other. In more complex cases in which the reactants carry substituents, secondary orbital effects are possible. These topics were explored during the experiment.

=== Prototypical Reaction ===

Firstly the HOMO and LUMO of cis-butadiene was visualized after optimization using the AM1 semi-empirical molecular orbital method. The HOMO is anti-symmetric with respect to the plane of symmetry through the molecule, and the LUMO is anti-symmetric.

{| class="wikitable"
!Cis-butadiene LUMO
!Cis-butadiene HOMO
|-
|
[[File:Butadiene LUMO.jpg|x250px]]

|
[[File:HOMO Butadiene.jpg|x250px]]
|}

Next an approximate transition structure was built using the optimized cis-butadiene and and optimized ethene molecule. The transition state structure was drawn so as to maximize the orbital overlap between the HOMO of cis-butadiene and the LUMO of ethene. The inter-fragment distances were set to be 2.2 Å and the point group to Cs. The structure was then optimized using the TS (Berny) method and the 3-21G basis set. This method was selected as for the prototypical reaction it was not necessary to use the freeze coordinate method, since the transition state geometry was a reasonably close guess. The calculation completed producing one imaginary frequency was obtained at -818.31 cm-1, indicating a transition state was reached. The point group was Cs. Afterwards an IRC calculation was also run in both directions, the plot is shown below.
{| class="wikitable"
!Structure
!IRC Plot
!Transition Structure
|-
|
[[File:But TS.jpg|x270px]]

|
[[File:IRC butadiene.jpg|x250px]]
|[[File:Butadiene TS.gif]]
|}
The imaginary frequency representing the transition state, shown above, indicates that the reaction proceeds in a concerted fashion, where the bonds are made and broken synchronously.The partly formed c-c bond lengths were 2.20940 Å and 2.20975, indicating that the transition state partial bonds are slightly longer than the approximate 2.2 Å used to build the transition state. '''TYPICAL SP3 BOND lengths etc discussion '''

<nowiki> </nowiki>The lowest positive frequency is shown below. Conversely here bond formation is happening in an asynchronous fashion.

[[File:Lowest pos frequ.gif]]

The HOMO and LUMO of the transition structure was then evaluated. The symmetrical LUMO and the anti-symmetrical HOMO are shown below.
{| class="wikitable"
!Anti-symmetrical HOMO
!Symmetrical LUMO
|-
|
[[File:AS HOMO CYCLOHEX.jpg|x270px]]

|
[[File:SYM LUMO CYCLOHEX.jpg|x270px]]

|}
It can be seen that the LUMO of the electron deficient ethene interacts with the HOMO of the butadiene to form the the HOMO above. This is the case for normal electron demand additions; as the energy gap between the LUMO of the diene and the HOMO of the dienophile is smaller than the converse gap between the LUMO of the dieneophile and the HOMO of the diene.

==== Maleic anhydride and Cyclohexa-1,3-diene Diels-Alder ====
The selectivity of the Diels-Alder reaction was then studied by evaluating the 2 possible transition states (endo and exo) that are possible in the reaction between maleic anhydride and cyclohexa-1,3-diene. The kinetically controlled reaction proceeds primarily via the endo transition state to give the kinetically favored endo product (also referred to as the endo rule). The two products can be seen below.

[[File:ENDO EXO Prods.jpg|x200px]]

Firstly maleic anhydride and a cyclohexa-1,3-diene molecules were optimized individually before making the transition structures. The endo guess transition structure was built first in GaussView, so that the π orbitals belonging to the carbonyl groups of the maleic anhydride were lying underneath the π orbitals of the cyclohexa-1,3-diene. The partial bonds between two fragments were set to be 2.2 Å again and the point group to Cs. Secondly optimizations were run, using two different basis sets for comparison: The Hartree Fock/ 3-21G level of theory and the AM1 semi-empirical molecular orbital method. In both cases an initial optimization was run using the frozen coordinate method, as it was likely that the transition structures were too dissimilar from reality to run a TS (Berny) calculation first. For both transition structures the partial c-c sp3 bond lengths were frozen to 2.2 Å and optimized, the bonds were then "unfrozen" as before and re-optimized using the TS (Berny) method. The point group remained Cs. One imaginary frequency was found at -605.60 cm-1; the corresponding frequency is shown below.

===== Hartree Fock Method =====
{| class="wikitable"
!Endo Structure
!Transition State
!Energy/ Hartrees
HF/3-21G
!HOMO
!LUMO
|-
|
[[File:ENDO TS.jpg|x250px]]

|
[[File:ENDO HF BERNY.gif]]

|<nowiki>-605.64958804</nowiki>
|
[[File:ENDO TS HOMO.jpg|x250px]]

|
[[File:Endo LUMO HF.jpg|x250px]]

|}

It can be seen that the LUMO is symmetrical with respect to the plane of symmetry, and the HOMO is anti-symmetrical.

Secondary orbital interactions.

The transition state animation shows the synchronicity of the bond formation.

Next the exo transition structure was made, this time ensuring the that the carbonyl groups of the anyhydride were pointing away from the the diene π bonds. The treatment was applied as above. Again the point group was Cs and an imaginary frequency was found at -647.53 cm-1.
{| class="wikitable"
!Exo Structure
!Transition State
!Energy/ Hartrees
HF/3-21G
!HOMO
!LUMO
|-
|
[[File:EXO TS Berny.jpg|x250px]]

|
[[File:EXO BERNY TS Freq.gif]]

|<nowiki>-605.60359125</nowiki>
|
[[File:EXO HOMO berny.jpg|x250px]]

|
[[File:EXO LUMO Berny.jpg|x250px]]

|}
Similarly here the bond forming is synchronous and facile. Both the HOMO and LUMO are anti-symmetrical with respect to the plane.

'''MORE DETAIL ON BONDING '''

===== AM1 Semi-empirical Molecular Orbital Method =====
The same process as above was followed, however this time using the semi-empirical method. The results are summarized below. Imaginary frequencies were found for the endo and exo transition states, they were ..... and -810.88 cm-1 respectively. The point groups for both were as before Cs.

{| class="wikitable"
!Structure
!Transition State
!Energy / Hartrees
Semi-empirical AM1
!HOMO
!LUMO
|-
|
|
|
|
|
|-
|EXO<gallery>
File:AM1 EXO TS.jpg
</gallery>
|<gallery>
File:EXO AM1 TS Vib.gif
</gallery>
|<nowiki>-0.05042001</nowiki>
|<gallery>
File:EXO AM1 Berny HOMO.jpg
</gallery>
|<gallery>
File:LUMO EXO AM1.jpg
</gallery>
|-
|ENDO<gallery>
File:AM1 ENDO TS IMAGE.jpg
</gallery>
|<gallery>
File:ENDO AM1 TS vib.gif
</gallery>
|<nowiki>-0.05119821</nowiki>
|<gallery>
File:ENDO HOMO AM1.jpg
</gallery>
|<gallery>
File:AM1 LUMO ENDO.jpg
</gallery>
|}
By comparison of the two methods it is again clear that using different methods does not have a great effect on the outcome of the geometry, but does however with regards to the energy.

A sketch was produced of both transition structures, and the bond lengths compared. By looking at the extent of bonding in each is is possible to evaluate the interactions between the molecules further.
{| class="wikitable"
!Exo sketch
!C10-C2 / Å
!C14 -15 / Å
!C10-C15 / Å
!C13-C14 / Å
|-
|<gallery>
File:Numbered EXO TS 1.jpg
</gallery>
|2.26065
|1.39758
|1.37003
|1.37003
|}
{| class="wikitable"
!Endo sketch
!C4 - C16/ Å
!C4 - C5 / Å
!C5-C6/ Å
!C6-C1 / Å
|-
|<gallery>
File:Numbered ENDO TS 1.jpg
</gallery>
|2.17057
|1.39436
|1.39679
|1.39436
|}
The majority of bond length in the table are in between that of a single sp3–sp3 c-c bond length (1.52 Å) and the sp3–sp2 c-c bond length (~134 Å for multiple bonds), these bond lengths correspond to the double bonds that are either being broken or formed during the reaction. The endo transition state is the more stable, as a result of this there is more bonding character between the two fragments.

File:Numbered ENDO TS 1.jpg

2015-11-05T20:41:58Z

Svp13:

File:Numbered EXO TS 1.jpg

2015-11-05T20:38:47Z

Svp13:

Rep:Mod:svp

2015-11-05T19:49:25Z

Svp13: /* Hartree Fock Method */

==Introduction==
The aim of this experiment was to characterise transition states for the Diels Alder cycloaddition and Cope rearrangement, computationally using the GaussView program. By doing so transition structures and the preferred reaction mechanism could be elucidated for the Cope rearrangement.

== The Cope Rearrangement Tutorial ==

The following tutorial explored the reactivity of 1,5-hexadiene in the Cope rearrangement. The mechanism by which the diene rearranges has previously been a topic of debate, owing to many computational and experimental studies. 1,5-hexadiene undergoes a pericyclic [3,3]-sigmatropic shift in a concerted fashion. The diene passes through either a chair or boat transition structure, the latter lying several kcal mol-1 higher in energy [2]. Previously computational studies have been ambiguous, making an agreement upon the mechanism difficult due to the flatness of potential energy surfaces belonging to the boat and chair transition states [3].In the following experiment activation energies were calculated by comparing the energies computed at the B3LYP/6-31G* level of theory, using the more sophisticated density functional theory (DFT) method. This method/basis set produces energies that comply with experimental data.

EXPERIMENT PICTURE -

=== Optimising the Reactants ===

==== “Anti2” conformation of 1,5- hexadiene ====
In Gaussview an “anti2” 1, 5- hexadiene molecule was built in an anti-peri-planar conformation. The molecule was cleaned before an optimisation was run at the Hartree Fock, 3-21G level of theory. This optimisation is run often as a pre-requisite to the more computationally expensive DFT (6-31G*) method. Cleaning before optimisation adjusts the geometry of the molecule in accordance with a set of parameters designed to produce a molecule that would be expected chemically.
Once optimised and all the calculations had converged, the structure was symmetrised and the point group was found to be Ci, on the highest tolerance setting. The energy of the molecule was found to be -231.69 a.u; this is in accordance with the energy provided in lab script appendix.
{| class="wikitable"
!Structure
!Point group
!Energy/ Hartrees
HF/3-21G
|-
|[[File:Anti structure.jpg|none|x200px]]
|Ci
|<nowiki>-231.69253522</nowiki>
|}

==== “Guache3” conformation of 1,5- hexadiene ====

Similarly to the anti-conformation the “gauche3” conformation was built and optimised at the Hartree Fock, 3-21G level of theory. The resultant energy was found to be less than the anti conformation and the given point group was C1 after symmetrising the molecule. The energy was again in agreement with the lab script value.

(Picture and table)

When calculating activation energies the lowest energy conformer of the reactant is used as a starting point. Chemical intuition would indicate that the “anti 2” conformation of 1,5- hexadiene would be the lowest in energy, due to steric effects. Studies such and including this have found the “guache 3” conformation to be the lowest. It has been suggested that this is due to an interaction between the vinyl proton and the c-c π electrons; such a bonding interaction accounts for the extra stability of the guache conformation. This effect is termed as the “CH-π” interaction (source).
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
HF/3-21G
|-
|<gallery>
File:Gauche 3.jpg
</gallery>
|C1
|<nowiki>-231.69266122</nowiki>
|}

=== DFT Optimisation of Reactants ===

The "Anti 2" 1,5- hexadiene molecule was re-optimised using the B3LYP/6-31G(d) level of theory using the DFT method. This is a higher level of theory than the Hartree fock 3-21G method; which is often done as a prerequisite to reduce the computational expense associated with the higher level of theory. After the second optimisation the point group of the molecule remained Ci. The energy was found to be -234. 61 a.u. in agreement with the value provided in the lab script appendix.

In order for the computed energies of the hexadiene molecules to be comparable with experimental data, a frequency calculation must be completed. After-which it is then possible to identify the critical point (a point at which all vibrational frequencies are real and positive). A frequency calculation was conducted on the 6-31G(d) optimised anti- hexadiene at the same level of theory. Once run, the vibrational frequencies of the molecule were checked to be all positive and real, and the infrared spectrum was generated.

A note of the following energies were taken from the the output file:
* The sum of electronic and zero-point energies (-234.416255 a.u.)
* The sum of electronic and thermal energies (-234.408963 a.u.)
* The sum of electronic and thermal enthalpies (-234.408019 a.u.)
* The sum of electronic and thermal free energies (-234.447872 a.u.)
The sum of electronic and zero point energies is similar to the experimental value, conducted at 0 K.
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
DFT/631G(d)
!IR spectrum
|-
|
[[File:Anti structure.jpg|x200px]]

|Ci
|<nowiki>-234.61171166</nowiki>
|
[[File:IR anti.jpg|x250px]]

|}

=== Optimizing the "Chair" and "Boat" Transition States ===

==== The Chair ====
In the following section the transition structures were built and optimised using a variety of methods:

(i)Computing the force constants at the start of the calculation.

(ii)Using the redundant coordinate editor.

(iii)Using the QST2 method.

Following optimization the intrinsic reaction coordinate (IRC) was run. This allows a path of minimum energy to be followed from a transition state structure down to the local minimum of the potential energy surface.

The chair transition state was composed of 2 allyl fragments, that were first optimized individually using the HF/3-21G level of theory before making each transition state in GaussView. The terminal carbon atoms of the allyl fragments were set to be 2.2 Å apart and were arranged into a chair like orientation. This guess transition state was then optimized using 2 different methods, both of which using Hartree Fock and the 3-21G basis set. It is necessary to use alternative methods to a typical minimization when optimizing a transition state as the program needs to be aware of the direction of negative curvature. '''(MORE DETAIL)'''

(i)The first method used was the TS (Berny) method; when optimizing using this method a good knowledge of the transition structure geometry is required. If the geometry is far from the true transition state geometry the optimization fails. The force constants in the this case were calculated once.

After the optimization had completed, one imaginary frequency at -818.81 cm-1 was found, indicating a transition structure had been reached. An imaginary frequency is produced at a transition state as a result of the resultant force constant being negative. As the frequency of motion is proportional to the square root of the force constant, an imaginary number is produced as a result.
{| class="wikitable"
!Transition State
!Structure
!Energy/ Hartrees
TS(Berny)
!Point Group
|-
|[[File:TS Frequency Chair.gif]]
|
[[File:Chair TS.jpg|x250px]]
|<nowiki>-231.6172118</nowiki>
|C2h
|}

(ii) The frozen coordinate method was then used, it can be used before running a TS (Berny) calculation. This is a suitable choice when the predicted transition state structure is not close to the real structure. The redundant coordinator editor was used to freeze the terminal c-c bond distances to 2.2 Å for the first optimization. Once the rest of the molecule had been optimized to a minimum the distances were "unfrozen" and a TS (Berny) calculation was run in a similar fashion as above except the force constants in this case were not calculated.
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
Frozen Coordinate
!Transition State
(Animation)
|-
|
[[File:TS Froze Chair.jpg|x250px]]
|C2h
|<nowiki>-231.61521115</nowiki>
|[[File:Chair Froze TS.gif]]
|}
Comparatively the two methods provide very similar results. The first although being quicker and less computationally expensive however would not suffice in situations where the transition state geometry deviated far from reality. The geometry of the two transition states was similar, with both belonging to the C2h point group. The bond forming/bond breaking lengths were 2.02047 Å after optimizing using the TS (Berny) alone and slightly longer after using the frozen coordinate method at 2.19939 Å.

==== The Boat ====
(iii) The boat transition structure was then optimized using the QST2 method.''' (MORE DETAIL)''' This method locates the transition structure based on the reactants and products. Such a method can be useful if the structure of the transition state is not known precisely.

Two of the previously optimized "Anti2", Ci 1,5- hexadiene molecules were arranged and numbered in a specific order, as shown below. As can be seen the optimization failed, the structure produced was highly dissociated and clearly does not show the expected boat transition structure.

{| class="wikitable"
!Starting Structure
!Structure after Optimization
|-
|
[[File:QST2 Numbered inc.jpg|x200px]]
|
[[File:QST2 Wrong TS.jpg|x200px]]

|}
The optimization above failed ad the QST2 method requires that the reactants and products be in a geometry close enough to the transition state.

A second optimization was then run, this time the dihedral angle was changed to 0° and the molecule was manipulated until molecules had geometry below was reached. The optimization was run again. It converged to the transition structure and one imaginary frequency (-839.86) was produced.
{| class="wikitable"
!Starting Structure
!Transition Structure
!Point group
!Energy/ Hartrees
QST2
!Transition State
(Animation)
|-
|
[[File:QST2 Starting.jpg|x250px]]
|
[[File:QST2 Boat TS.jpg|x250px]]
|C2V
|<nowiki>-231.60280239</nowiki>
|[[File:Boat TS QST2.gif]]
|
|}
It is not possible at this stage to decipher which of the conformers of 1,5- hexadiene corresponds to which transition state. It it however possible using and IRC to follow the minimum energy path of a transition structure down to its local minimum. It does so by travelling along the steepest part of the potential energy surface.

==== IRC Calculation ====
Next an IRC was conducted on the chair transition state structure previously optimized using the frozen coordinate method. The number of steps within an IRC calculation may be set; in this case an IRC was run in the forward direction due to the symmetrical nature of the reaction coordinate. The number of steps was set to 50.

{| class="wikitable"
!IRC plot
!Final Geometry after IRC Calculation
|-
|
[[File:IRC Chair plot.png|x250px]]
|
[[File:Step 50 IRC chair.jpg|x250px]]
|}
It can be seen from the plot that once the calculation had finished the structure had not reached a minimum geometry. From the IRC you can see the energy plateau, however it had not reached a minimum. This suggests there were too few steps run, it can however be difficult to know the correct number of steps to use, as if too many are used the coordinate may veer off and an alternative energy path may be followed. In order to obtain the minimum a normal minimization was run using Hartree Fock and the 3-21G basis set. The final structure was that of the chair transition state, and the energy was found to be -231.692239 a.u. This is similar to both of the "gauche2" and "gauche3" conformers of 1,5 -hexadiene energies, visually it could be seen to resemble the "gauche3" conformer, belonging to the C1 point group.

==== Activation Energies ====
Lastly the activation energies for the reaction via both transition sates were calculated. Both transition structure were re-optimized using the DFT/ B3LYP/6-31G(d) level of theory. Frequency calculations were conducted on the structures previously optimized at the Hartree Fock 3-21G level.
{| class="wikitable"
!Structure
!Energy 3-21G/
Hartrees
!Energy 6-31G(d)/
Hartrees
!Energy + Zero Point
Energy 3-21G/

Hartrees (at 0 K)
!'''Sum of Electronic '''and Thermal Energies 3-21G

(at 298.15 K)
!Energy + Zero Point
Energy 6-31G(d)/

Hartrees (at 0 K)
!'''Sum of Electronic'''and Thermal Energies 6-31G(d)

(at 298.15 K)
!Point Group
3-21G , 631G(d)
|-
|"Anti2" conformer
|<nowiki>-231.69253522</nowiki>
|<nowiki>-234.61171166</nowiki>
|<nowiki>-231.539611</nowiki>
|<nowiki>-231.532567</nowiki>
|<nowiki>-234.468755</nowiki>
|<nowiki>-234.461963</nowiki>
|Ci , Ci
|-
|Boat TS
|<nowiki>-231.60280239</nowiki>
|<nowiki>-234.54307876</nowiki>
|<nowiki>-231.450924</nowiki>
|<nowiki>-231.445294</nowiki>
|<nowiki>-234.402360</nowiki>
|<nowiki>-234.396016</nowiki>
|C2v , C2v
|-
|Chair TS
|<nowiki>-231.61721180</nowiki>
|<nowiki>-234.55692628</nowiki>
|<nowiki>-231.466701</nowiki>
|<nowiki>-231.461341</nowiki>
|<nowiki>-234.416255</nowiki>
|<nowiki>-234.408999</nowiki>
|C2v , C2v
|}
The activation energies were calculated by finding the difference between the reactant energy and the transition state energy, these are shown below in Kcal mol-1.
{| class="wikitable"
!
!HF/ 3-21G
at 0 K
!B3LYP/ 6-31G(d)
at 0 K
!HF/ 3-21G
at 298.15 K
!B3LYP/ 6-31G(d)
at 298.15 K
!Experiment / Kcal mol-1at 0 K
|-
|ΔE '''(Chair)''' / Kcal mol-1
|45.75
|32.57
|44.72
|33.24
|33.5 ± 0.5
|-
|ΔE '''(Boat)''' / Kcal mol-1
|55.65
|41.66
|54.84
|41.38
|44.7 ± 2.0
|}
Overall the results match the expected computed values reasonably well. It can be seen that the geometry remains similar for both basis sets; whilst the energies differ considerably. It is clear that either basis set is an adequate tool for examining the geometry of molecules however when comparing energies the higher level of theory proves to be more accurate. For both levels of theory however there appears to be a general overestimation of the activation energy when computing them with GuassView as opposed to obtaining them experimentally. This overestimation reflects the approximations the program makes. In particular the computation of just one molecule introduces error, as inter-molecular forces are not taken into account. There are also calculations that may be run at a higher level of theory that would improve the accuracy of the results.

== The Diels-Alder Cycloaddition ==
The following part of the experiment explored the Diels-Alder cycloaddition by investigating the transition state structures and analyzing molecular orbitals. The Diels-Alder cycloaddition is [4+2] pericyclic addition, in which two conjugated π systems add to form a ring. This occurs in a concerted fashion via a cyclic transition state. Heat is not necessarily required to drive the reaction as the formation of two new sigma bonds over the loss of two π bonds is favored, however heat is often use to drive the reaction. The prototypical example of ethene (the dienophile) and cis-butadiene (the diene) is shown below.

[[File:DA.jpg|x200px]]

Diels-Alder cycloadditons may be termed normal electron demand additions, in which the diene is electron rich and the dienophile is electron deficient; or as inverse electron demand additions if reverse is the case. The electronic properties dictate the interactions between the HOMO's and LUMO's of a given reaction. For an allowed reaction the HOMO of one of the reactants must interact with the LUMO of the other. In more complex cases in which the reactants carry substituents, secondary orbital effects are possible. These topics were explored during the experiment.

=== Prototypical Reaction ===

Firstly the HOMO and LUMO of cis-butadiene was visualized after optimization using the AM1 semi-empirical molecular orbital method. The HOMO is anti-symmetric with respect to the plane of symmetry through the molecule, and the LUMO is anti-symmetric.

{| class="wikitable"
!Cis-butadiene LUMO
!Cis-butadiene HOMO
|-
|
[[File:Butadiene LUMO.jpg|x250px]]

|
[[File:HOMO Butadiene.jpg|x250px]]
|}

Next an approximate transition structure was built using the optimized cis-butadiene and and optimized ethene molecule. The transition state structure was drawn so as to maximize the orbital overlap between the HOMO of cis-butadiene and the LUMO of ethene. The inter-fragment distances were set to be 2.2 Å and the point group to Cs. The structure was then optimized using the TS (Berny) method and the 3-21G basis set. This method was selected as for the prototypical reaction it was not necessary to use the freeze coordinate method, since the transition state geometry was a reasonably close guess. The calculation completed producing one imaginary frequency was obtained at -818.31 cm-1, indicating a transition state was reached. The point group was Cs. Afterwards an IRC calculation was also run in both directions, the plot is shown below.
{| class="wikitable"
!Structure
!IRC Plot
!Transition Structure
|-
|
[[File:But TS.jpg|x270px]]

|
[[File:IRC butadiene.jpg|x250px]]
|[[File:Butadiene TS.gif]]
|}
The imaginary frequency representing the transition state, shown above, indicates that the reaction proceeds in a concerted fashion, where the bonds are made and broken synchronously.The partly formed c-c bond lengths were 2.20940 Å and 2.20975, indicating that the transition state partial bonds are slightly longer than the approximate 2.2 Å used to build the transition state. '''TYPICAL SP3 BOND lengths etc discussion '''

<nowiki> </nowiki>The lowest positive frequency is shown below. Conversely here bond formation is happening in an asynchronous fashion.

[[File:Lowest pos frequ.gif]]

The HOMO and LUMO of the transition structure was then evaluated. The symmetrical LUMO and the anti-symmetrical HOMO are shown below.
{| class="wikitable"
!Anti-symmetrical HOMO
!Symmetrical LUMO
|-
|
[[File:AS HOMO CYCLOHEX.jpg|x270px]]

|
[[File:SYM LUMO CYCLOHEX.jpg|x270px]]

|}
It can be seen that the LUMO of the electron deficient ethene interacts with the HOMO of the butadiene to form the the HOMO above. This is the case for normal electron demand additions; as the energy gap between the LUMO of the diene and the HOMO of the dienophile is smaller than the converse gap between the LUMO of the dieneophile and the HOMO of the diene.

==== Maleic anhydride and Cyclohexa-1,3-diene Diels-Alder ====
The selectivity of the Diels-Alder reaction was then studied by evaluating the 2 possible transition states (endo and exo) that are possible in the reaction between maleic anhydride and cyclohexa-1,3-diene. The kinetically controlled reaction proceeds primarily via the endo transition state to give the kinetically favored endo product (also referred to as the endo rule). The two products can be seen below.

[[File:ENDO EXO Prods.jpg|x200px]]

Firstly maleic anhydride and a cyclohexa-1,3-diene molecules were optimized individually before making the transition structures. The endo guess transition structure was built first in GaussView, so that the π orbitals belonging to the carbonyl groups of the maleic anhydride were lying underneath the π orbitals of the cyclohexa-1,3-diene. The partial bonds between two fragments were set to be 2.2 Å again and the point group to Cs. Secondly optimizations were run, using two different basis sets for comparison: The Hartree Fock/ 3-21G level of theory and the AM1 semi-empirical molecular orbital method. In both cases an initial optimization was run using the frozen coordinate method, as it was likely that the transition structures were too dissimilar from reality to run a TS (Berny) calculation first. For both transition structures the partial c-c sp3 bond lengths were frozen to 2.2 Å and optimized, the bonds were then "unfrozen" as before and re-optimized using the TS (Berny) method. The point group remained Cs. One imaginary frequency was found at -605.60 cm-1; the corresponding frequency is shown below.

===== Hartree Fock Method =====
{| class="wikitable"
!Endo Structure
!Transition State
!Energy/ Hartrees
HF/3-21G
!HOMO
!LUMO
|-
|
[[File:ENDO TS.jpg|x250px]]

|
[[File:ENDO HF BERNY.gif]]

|<nowiki>-605.60359125</nowiki>
|
[[File:ENDO TS HOMO.jpg|x250px]]

|
[[File:Endo LUMO HF.jpg|x250px]]

|}

It can be seen that the LUMO is symmetrical with respect to the plane of symmetry, and the HOMO is anti-symmetrical.

Secondary orbital interactions.

The transition state animation shows the synchronicity of the bond formation.

Next the exo transition structure was made, this time ensuring the that the carbonyl groups of the anyhydride were pointing away from the the diene π bonds. The treatment was applied as above. Again the point group was Cs and an imaginary frequency was found at -647.53 cm-1.
{| class="wikitable"
!Exo Structure
!Transition State
!Energy/ Hartrees
HF/3-21G
!HOMO
!LUMO
|-
|
[[File:EXO TS Berny.jpg|x250px]]

|
[[File:EXO BERNY TS Freq.gif]]

|<nowiki>-605.60359125</nowiki>
|
[[File:EXO HOMO berny.jpg|x250px]]

|
[[File:EXO LUMO Berny.jpg|x250px]]

|}
Similarly here the bond forming is synchronous and facile. Both the HOMO and LUMO are anti-symmetrical with respect to the plane.

'''MORE DETAIL ON BONDING '''

===== AM1 Semi-empirical Molecular Orbital Method =====
The same process as above was followed, however this time using the semi-empirical method. The results are summarized below. Imaginary frequencies were found for the endo and exo transition states, they were ..... and -810.88 cm-1 respectively. The point groups for both were as before Cs.

{| class="wikitable"
!Structure
!Transition State
!Energy / Hartrees
Semi-empirical AM1
!HOMO
!LUMO
|-
|
|
|
|
|
|-
|EXO<gallery>
File:AM1 EXO TS.jpg
</gallery>
|<gallery>
File:EXO AM1 TS Vib.gif
</gallery>
|<nowiki>-0.05042001</nowiki>
|<gallery>
File:EXO AM1 Berny HOMO.jpg
</gallery>
|<gallery>
File:LUMO EXO AM1.jpg
</gallery>
|-
|ENDO<gallery>
File:AM1 ENDO TS IMAGE.jpg
</gallery>
|<gallery>
File:ENDO AM1 TS vib.gif
</gallery>
|<nowiki>-0.05011982</nowiki>
|<gallery>
File:ENDO HOMO AM1.jpg
</gallery>
|<gallery>
File:AM1 LUMO ENDO.jpg
</gallery>
|}
By comparison of the two methods it is again clear that using different methods does not have a great effect on the outcome of the geometry, but does however with regards to the energy.

Rep:Mod:svp

2015-11-05T19:27:31Z

Svp13:

==Introduction==
The aim of this experiment was to characterise transition states for the Diels Alder cycloaddition and Cope rearrangement, computationally using the GaussView program. By doing so transition structures and the preferred reaction mechanism could be elucidated for the Cope rearrangement.

== The Cope Rearrangement Tutorial ==

The following tutorial explored the reactivity of 1,5-hexadiene in the Cope rearrangement. The mechanism by which the diene rearranges has previously been a topic of debate, owing to many computational and experimental studies. 1,5-hexadiene undergoes a pericyclic [3,3]-sigmatropic shift in a concerted fashion. The diene passes through either a chair or boat transition structure, the latter lying several kcal mol-1 higher in energy [2]. Previously computational studies have been ambiguous, making an agreement upon the mechanism difficult due to the flatness of potential energy surfaces belonging to the boat and chair transition states [3].In the following experiment activation energies were calculated by comparing the energies computed at the B3LYP/6-31G* level of theory, using the more sophisticated density functional theory (DFT) method. This method/basis set produces energies that comply with experimental data.

EXPERIMENT PICTURE -

=== Optimising the Reactants ===

==== “Anti2” conformation of 1,5- hexadiene ====
In Gaussview an “anti2” 1, 5- hexadiene molecule was built in an anti-peri-planar conformation. The molecule was cleaned before an optimisation was run at the Hartree Fock, 3-21G level of theory. This optimisation is run often as a pre-requisite to the more computationally expensive DFT (6-31G*) method. Cleaning before optimisation adjusts the geometry of the molecule in accordance with a set of parameters designed to produce a molecule that would be expected chemically.
Once optimised and all the calculations had converged, the structure was symmetrised and the point group was found to be Ci, on the highest tolerance setting. The energy of the molecule was found to be -231.69 a.u; this is in accordance with the energy provided in lab script appendix.
{| class="wikitable"
!Structure
!Point group
!Energy/ Hartrees
HF/3-21G
|-
|[[File:Anti structure.jpg|none|x200px]]
|Ci
|<nowiki>-231.69253522</nowiki>
|}

==== “Guache3” conformation of 1,5- hexadiene ====

Similarly to the anti-conformation the “gauche3” conformation was built and optimised at the Hartree Fock, 3-21G level of theory. The resultant energy was found to be less than the anti conformation and the given point group was C1 after symmetrising the molecule. The energy was again in agreement with the lab script value.

(Picture and table)

When calculating activation energies the lowest energy conformer of the reactant is used as a starting point. Chemical intuition would indicate that the “anti 2” conformation of 1,5- hexadiene would be the lowest in energy, due to steric effects. Studies such and including this have found the “guache 3” conformation to be the lowest. It has been suggested that this is due to an interaction between the vinyl proton and the c-c π electrons; such a bonding interaction accounts for the extra stability of the guache conformation. This effect is termed as the “CH-π” interaction (source).
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
HF/3-21G
|-
|<gallery>
File:Gauche 3.jpg
</gallery>
|C1
|<nowiki>-231.69266122</nowiki>
|}

=== DFT Optimisation of Reactants ===

The "Anti 2" 1,5- hexadiene molecule was re-optimised using the B3LYP/6-31G(d) level of theory using the DFT method. This is a higher level of theory than the Hartree fock 3-21G method; which is often done as a prerequisite to reduce the computational expense associated with the higher level of theory. After the second optimisation the point group of the molecule remained Ci. The energy was found to be -234. 61 a.u. in agreement with the value provided in the lab script appendix.

In order for the computed energies of the hexadiene molecules to be comparable with experimental data, a frequency calculation must be completed. After-which it is then possible to identify the critical point (a point at which all vibrational frequencies are real and positive). A frequency calculation was conducted on the 6-31G(d) optimised anti- hexadiene at the same level of theory. Once run, the vibrational frequencies of the molecule were checked to be all positive and real, and the infrared spectrum was generated.

A note of the following energies were taken from the the output file:
* The sum of electronic and zero-point energies (-234.416255 a.u.)
* The sum of electronic and thermal energies (-234.408963 a.u.)
* The sum of electronic and thermal enthalpies (-234.408019 a.u.)
* The sum of electronic and thermal free energies (-234.447872 a.u.)
The sum of electronic and zero point energies is similar to the experimental value, conducted at 0 K.
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
DFT/631G(d)
!IR spectrum
|-
|
[[File:Anti structure.jpg|x200px]]

|Ci
|<nowiki>-234.61171166</nowiki>
|
[[File:IR anti.jpg|x250px]]

|}

=== Optimizing the "Chair" and "Boat" Transition States ===

==== The Chair ====
In the following section the transition structures were built and optimised using a variety of methods:

(i)Computing the force constants at the start of the calculation.

(ii)Using the redundant coordinate editor.

(iii)Using the QST2 method.

Following optimization the intrinsic reaction coordinate (IRC) was run. This allows a path of minimum energy to be followed from a transition state structure down to the local minimum of the potential energy surface.

The chair transition state was composed of 2 allyl fragments, that were first optimized individually using the HF/3-21G level of theory before making each transition state in GaussView. The terminal carbon atoms of the allyl fragments were set to be 2.2 Å apart and were arranged into a chair like orientation. This guess transition state was then optimized using 2 different methods, both of which using Hartree Fock and the 3-21G basis set. It is necessary to use alternative methods to a typical minimization when optimizing a transition state as the program needs to be aware of the direction of negative curvature. '''(MORE DETAIL)'''

(i)The first method used was the TS (Berny) method; when optimizing using this method a good knowledge of the transition structure geometry is required. If the geometry is far from the true transition state geometry the optimization fails. The force constants in the this case were calculated once.

After the optimization had completed, one imaginary frequency at -818.81 cm-1 was found, indicating a transition structure had been reached. An imaginary frequency is produced at a transition state as a result of the resultant force constant being negative. As the frequency of motion is proportional to the square root of the force constant, an imaginary number is produced as a result.
{| class="wikitable"
!Transition State
!Structure
!Energy/ Hartrees
TS(Berny)
!Point Group
|-
|[[File:TS Frequency Chair.gif]]
|
[[File:Chair TS.jpg|x250px]]
|<nowiki>-231.6172118</nowiki>
|C2h
|}

(ii) The frozen coordinate method was then used, it can be used before running a TS (Berny) calculation. This is a suitable choice when the predicted transition state structure is not close to the real structure. The redundant coordinator editor was used to freeze the terminal c-c bond distances to 2.2 Å for the first optimization. Once the rest of the molecule had been optimized to a minimum the distances were "unfrozen" and a TS (Berny) calculation was run in a similar fashion as above except the force constants in this case were not calculated.
{| class="wikitable"
!Structure
!Point Group
!Energy/ Hartrees
Frozen Coordinate
!Transition State
(Animation)
|-
|
[[File:TS Froze Chair.jpg|x250px]]
|C2h
|<nowiki>-231.61521115</nowiki>
|[[File:Chair Froze TS.gif]]
|}
Comparatively the two methods provide very similar results. The first although being quicker and less computationally expensive however would not suffice in situations where the transition state geometry deviated far from reality. The geometry of the two transition states was similar, with both belonging to the C2h point group. The bond forming/bond breaking lengths were 2.02047 Å after optimizing using the TS (Berny) alone and slightly longer after using the frozen coordinate method at 2.19939 Å.

==== The Boat ====
(iii) The boat transition structure was then optimized using the QST2 method.''' (MORE DETAIL)''' This method locates the transition structure based on the reactants and products. Such a method can be useful if the structure of the transition state is not known precisely.

Two of the previously optimized "Anti2", Ci 1,5- hexadiene molecules were arranged and numbered in a specific order, as shown below. As can be seen the optimization failed, the structure produced was highly dissociated and clearly does not show the expected boat transition structure.

{| class="wikitable"
!Starting Structure
!Structure after Optimization
|-
|
[[File:QST2 Numbered inc.jpg|x200px]]
|
[[File:QST2 Wrong TS.jpg|x200px]]

|}
The optimization above failed ad the QST2 method requires that the reactants and products be in a geometry close enough to the transition state.

A second optimization was then run, this time the dihedral angle was changed to 0° and the molecule was manipulated until molecules had geometry below was reached. The optimization was run again. It converged to the transition structure and one imaginary frequency (-839.86) was produced.
{| class="wikitable"
!Starting Structure
!Transition Structure
!Point group
!Energy/ Hartrees
QST2
!Transition State
(Animation)
|-
|
[[File:QST2 Starting.jpg|x250px]]
|
[[File:QST2 Boat TS.jpg|x250px]]
|C2V
|<nowiki>-231.60280239</nowiki>
|[[File:Boat TS QST2.gif]]
|
|}
It is not possible at this stage to decipher which of the conformers of 1,5- hexadiene corresponds to which transition state. It it however possible using and IRC to follow the minimum energy path of a transition structure down to its local minimum. It does so by travelling along the steepest part of the potential energy surface.

==== IRC Calculation ====
Next an IRC was conducted on the chair transition state structure previously optimized using the frozen coordinate method. The number of steps within an IRC calculation may be set; in this case an IRC was run in the forward direction due to the symmetrical nature of the reaction coordinate. The number of steps was set to 50.

{| class="wikitable"
!IRC plot
!Final Geometry after IRC Calculation
|-
|
[[File:IRC Chair plot.png|x250px]]
|
[[File:Step 50 IRC chair.jpg|x250px]]
|}
It can be seen from the plot that once the calculation had finished the structure had not reached a minimum geometry. From the IRC you can see the energy plateau, however it had not reached a minimum. This suggests there were too few steps run, it can however be difficult to know the correct number of steps to use, as if too many are used the coordinate may veer off and an alternative energy path may be followed. In order to obtain the minimum a normal minimization was run using Hartree Fock and the 3-21G basis set. The final structure was that of the chair transition state, and the energy was found to be -231.692239 a.u. This is similar to both of the "gauche2" and "gauche3" conformers of 1,5 -hexadiene energies, visually it could be seen to resemble the "gauche3" conformer, belonging to the C1 point group.

==== Activation Energies ====
Lastly the activation energies for the reaction via both transition sates were calculated. Both transition structure were re-optimized using the DFT/ B3LYP/6-31G(d) level of theory. Frequency calculations were conducted on the structures previously optimized at the Hartree Fock 3-21G level.
{| class="wikitable"
!Structure
!Energy 3-21G/
Hartrees
!Energy 6-31G(d)/
Hartrees
!Energy + Zero Point
Energy 3-21G/

Hartrees (at 0 K)
!'''Sum of Electronic '''and Thermal Energies 3-21G

(at 298.15 K)
!Energy + Zero Point
Energy 6-31G(d)/

Hartrees (at 0 K)
!'''Sum of Electronic'''and Thermal Energies 6-31G(d)

(at 298.15 K)
!Point Group
3-21G , 631G(d)
|-
|"Anti2" conformer
|<nowiki>-231.69253522</nowiki>
|<nowiki>-234.61171166</nowiki>
|<nowiki>-231.539611</nowiki>
|<nowiki>-231.532567</nowiki>
|<nowiki>-234.468755</nowiki>
|<nowiki>-234.461963</nowiki>
|Ci , Ci
|-
|Boat TS
|<nowiki>-231.60280239</nowiki>
|<nowiki>-234.54307876</nowiki>
|<nowiki>-231.450924</nowiki>
|<nowiki>-231.445294</nowiki>
|<nowiki>-234.402360</nowiki>
|<nowiki>-234.396016</nowiki>
|C2v , C2v
|-
|Chair TS
|<nowiki>-231.61721180</nowiki>
|<nowiki>-234.55692628</nowiki>
|<nowiki>-231.466701</nowiki>
|<nowiki>-231.461341</nowiki>
|<nowiki>-234.416255</nowiki>
|<nowiki>-234.408999</nowiki>
|C2v , C2v
|}
The activation energies were calculated by finding the difference between the reactant energy and the transition state energy, these are shown below in Kcal mol-1.
{| class="wikitable"
!
!HF/ 3-21G
at 0 K
!B3LYP/ 6-31G(d)
at 0 K
!HF/ 3-21G
at 298.15 K
!B3LYP/ 6-31G(d)
at 298.15 K
!Experiment / Kcal mol-1at 0 K
|-
|ΔE '''(Chair)''' / Kcal mol-1
|45.75
|32.57
|44.72
|33.24
|33.5 ± 0.5
|-
|ΔE '''(Boat)''' / Kcal mol-1
|55.65
|41.66
|54.84
|41.38
|44.7 ± 2.0
|}
Overall the results match the expected computed values reasonably well. It can be seen that the geometry remains similar for both basis sets; whilst the energies differ considerably. It is clear that either basis set is an adequate tool for examining the geometry of molecules however when comparing energies the higher level of theory proves to be more accurate. For both levels of theory however there appears to be a general overestimation of the activation energy when computing them with GuassView as opposed to obtaining them experimentally. This overestimation reflects the approximations the program makes. In particular the computation of just one molecule introduces error, as inter-molecular forces are not taken into account. There are also calculations that may be run at a higher level of theory that would improve the accuracy of the results.

== The Diels-Alder Cycloaddition ==
The following part of the experiment explored the Diels-Alder cycloaddition by investigating the transition state structures and analyzing molecular orbitals. The Diels-Alder cycloaddition is [4+2] pericyclic addition, in which two conjugated π systems add to form a ring. This occurs in a concerted fashion via a cyclic transition state. Heat is not necessarily required to drive the reaction as the formation of two new sigma bonds over the loss of two π bonds is favored, however heat is often use to drive the reaction. The prototypical example of ethene (the dienophile) and cis-butadiene (the diene) is shown below.

[[File:DA.jpg|x200px]]

Diels-Alder cycloadditons may be termed normal electron demand additions, in which the diene is electron rich and the dienophile is electron deficient; or as inverse electron demand additions if reverse is the case. The electronic properties dictate the interactions between the HOMO's and LUMO's of a given reaction. For an allowed reaction the HOMO of one of the reactants must interact with the LUMO of the other. In more complex cases in which the reactants carry substituents, secondary orbital effects are possible. These topics were explored during the experiment.

=== Prototypical Reaction ===

Firstly the HOMO and LUMO of cis-butadiene was visualized after optimization using the AM1 semi-empirical molecular orbital method. The HOMO is anti-symmetric with respect to the plane of symmetry through the molecule, and the LUMO is anti-symmetric.

{| class="wikitable"
!Cis-butadiene LUMO
!Cis-butadiene HOMO
|-
|
[[File:Butadiene LUMO.jpg|x250px]]

|
[[File:HOMO Butadiene.jpg|x250px]]
|}

Next an approximate transition structure was built using the optimized cis-butadiene and and optimized ethene molecule. The transition state structure was drawn so as to maximize the orbital overlap between the HOMO of cis-butadiene and the LUMO of ethene. The inter-fragment distances were set to be 2.2 Å and the point group to Cs. The structure was then optimized using the TS (Berny) method and the 3-21G basis set. This method was selected as for the prototypical reaction it was not necessary to use the freeze coordinate method, since the transition state geometry was a reasonably close guess. The calculation completed producing one imaginary frequency was obtained at -818.31 cm-1, indicating a transition state was reached. The point group was Cs. Afterwards an IRC calculation was also run in both directions, the plot is shown below.
{| class="wikitable"
!Structure
!IRC Plot
!Transition Structure
|-
|
[[File:But TS.jpg|x270px]]

|
[[File:IRC butadiene.jpg|x250px]]
|[[File:Butadiene TS.gif]]
|}
The imaginary frequency representing the transition state, shown above, indicates that the reaction proceeds in a concerted fashion, where the bonds are made and broken synchronously.The partly formed c-c bond lengths were 2.20940 Å and 2.20975, indicating that the transition state partial bonds are slightly longer than the approximate 2.2 Å used to build the transition state. '''TYPICAL SP3 BOND lengths etc discussion '''

<nowiki> </nowiki>The lowest positive frequency is shown below. Conversely here bond formation is happening in an asynchronous fashion.

[[File:Lowest pos frequ.gif]]

The HOMO and LUMO of the transition structure was then evaluated. The symmetrical LUMO and the anti-symmetrical HOMO are shown below.
{| class="wikitable"
!Anti-symmetrical HOMO
!Symmetrical LUMO
|-
|
[[File:AS HOMO CYCLOHEX.jpg|x270px]]

|
[[File:SYM LUMO CYCLOHEX.jpg|x270px]]

|}
It can be seen that the LUMO of the electron deficient ethene interacts with the HOMO of the butadiene to form the the HOMO above. This is the case for normal electron demand additions; as the energy gap between the LUMO of the diene and the HOMO of the dienophile is smaller than the converse gap between the LUMO of the dieneophile and the HOMO of the diene.

==== Maleic anhydride and Cyclohexa-1,3-diene Diels-Alder ====
The selectivity of the Diels-Alder reaction was then studied by evaluating the 2 possible transition states (endo and exo) that are possible in the reaction between maleic anhydride and cyclohexa-1,3-diene. The kinetically controlled reaction proceeds primarily via the endo transition state to give the kinetically favored endo product (also referred to as the endo rule). The two products can be seen below.

[[File:ENDO EXO Prods.jpg|x200px]]

Firstly maleic anhydride and a cyclohexa-1,3-diene molecules were optimized individually before making the transition structures. The endo guess transition structure was built first in GaussView, so that the π orbitals belonging to the carbonyl groups of the maleic anhydride were lying underneath the π orbitals of the cyclohexa-1,3-diene. The partial bonds between two fragments were set to be 2.2 Å again and the point group to Cs. Secondly optimizations were run, using two different basis sets for comparison: The Hartree Fock/ 3-21G level of theory and the AM1 semi-empirical molecular orbital method. In both cases an initial optimization was run using the frozen coordinate method, as it was likely that the transition structures were too dissimilar from reality to run a TS (Berny) calculation first. For both transition structures the partial c-c sp3 bond lengths were frozen to 2.2 Å and optimized, the bonds were then "unfrozen" as before and re-optimized using the TS (Berny) method. The point group remained Cs. One imaginary frequency was found at -605.60 cm-1; the corresponding frequency is shown below.

===== Hartree Fock Method =====
{| class="wikitable"
!Endo Structure
!Transition State
!Energy/ Hartrees
HF/3-21G
!HOMO
!LUMO
|-
|<gallery>
File:ENDO TS.jpg
</gallery>
|<gallery>
File:ENDO HF BERNY.gif
</gallery>
|<nowiki>-605.60359125</nowiki>
|<gallery>
File:ENDO TS HOMO.jpg
</gallery>
|<gallery>
File:Endo LUMO HF.jpg
</gallery>
|}

It can be seen that the LUMO is symmetrical with respect to the plane of symmetry, and the HOMO is anti-symmetrical.

Secondary orbital interactions.

The transition state animation shows the synchronicity of the bond formation.

Next the exo transition structure was made, this time ensuring the that the carbonyl groups of the anyhydride were pointing away from the the diene π bonds. The treatment was applied as above. Again the point group was Cs and an imaginary frequency was found at -647.53 cm-1.
{| class="wikitable"
!Exo Structure
!Transition State
!Energy/ Hartrees
HF/3-21G
!HOMO
!LUMO
|-
|<gallery>
File:EXO TS Berny.jpg
</gallery>
|<gallery>
File:EXO BERNY TS Freq.gif
</gallery>
|<nowiki>-605.60359125</nowiki>
|<gallery>
File:EXO HOMO berny.jpg
</gallery>
|<gallery>
File:EXO LUMO Berny.jpg
</gallery>
|}
Similarly here the bond forming is synchronous and facile. Both the HOMO and LUMO are anti-symmetrical with respect to the plane.

'''MORE DETAIL ON BONDING '''

===== AM1 Semi-empirical Molecular Orbital Method =====
The same process as above was followed, however this time using the semi-empirical method. The results are summarized below. Imaginary frequencies were found for the endo and exo transition states, they were ..... and -810.88 cm-1 respectively. The point groups for both were as before Cs.

{| class="wikitable"
!Structure
!Transition State
!Energy / Hartrees
Semi-empirical AM1
!HOMO
!LUMO
|-
|
|
|
|
|
|-
|EXO<gallery>
File:AM1 EXO TS.jpg
</gallery>
|<gallery>
File:EXO AM1 TS Vib.gif
</gallery>
|<nowiki>-0.05042001</nowiki>
|<gallery>
File:EXO AM1 Berny HOMO.jpg
</gallery>
|<gallery>
File:LUMO EXO AM1.jpg
</gallery>
|-
|ENDO<gallery>
File:AM1 ENDO TS IMAGE.jpg
</gallery>
|<gallery>
File:ENDO AM1 TS vib.gif
</gallery>
|<nowiki>-0.05011982</nowiki>
|<gallery>
File:ENDO HOMO AM1.jpg
</gallery>
|<gallery>
File:AM1 LUMO ENDO.jpg
</gallery>
|}
By comparison of the two methods it is again clear that using different methods does not have a great effect on the outcome of the geometry, but does however with regards to the energy.

File:Gauche 3.jpg

2015-11-05T19:26:40Z

Svp13: Svp13 uploaded a new version of File:Gauche 3.jpg

Rep:Mod:svp

2015-11-05T19:26:01Z

2015-11-05T18:26:34Z

2015-11-05T17:29:56Z

Svp13: Svp13 uploaded a new version of File:ENDO TS HOMO.jpg

File:ENDO HF BERNY.gif

2015-11-05T17:27:33Z

Svp13: