ChemWiki - User contributions [en]

Rep:Mod:kitten

2014-03-21T16:26:53Z

Da1111:

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data. Calculations are shown in the log files provided.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. <ref name="cope">IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997) </ref> and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature <ref name="conf">B. W. Gung, Z. Zhu, and R. A. Fouch, ''J. Am. Chem. Soc.'', '''1995''', ''117'', 1783-1788</ref>
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

[[File:ANTICIATTEMPT2V3FREQ.LOG]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]
[[File:CHAIRTSGUESSV1IRCATTEMPT1.LOG]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

[[File:CHAIRTSGUESSV1REOPT.LOG]]
[[File:CHAIRTSGUESSV2CONTREOPT.LOG]]
[[File:BOATTSREOPTBERNY.LOG]]

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.<ref name="cope" />

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg|200px]] || [[Image:cisbutadiene_MO12.jpg|200px]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

[[File:CISBUTADIENE_OPT.LOG]]

===Transition State Geometry for Simple Diels-Alder Reaction===
The ethene MOs were also investigated and the symmetries reported in the table below.

{| class="wikitable" border="1"
|+ HOMO and LUMO of ethene
! !! HOMO !! LUMO
|-
| Image || [[Image:etheneHOMO.jpg|200px]] || [[Image:etheneLUMO.jpg|200px]]
|-
| Symmetry with respect to plane || symmetric || antisymmetric
|}

The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of 2.12 Å. An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at -956 cm-1 which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous and shows the reaction mechanism of the two molecules coming together, unlike the smallest positive frequency at 147 cm-1 which shows a rocking motion that could potentially result in asynchronous bond forming.

[[Image:Diels_alder_TS.gif|frame|center|200px|Animation of imaginary frequency of Diels Alder transition state<jmol><jmolAppletButton><uploadedFileContents>Diels_alder_berny_TSv2HOMO.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[Image:Diels_alder_TS_positive_frequency.gif|frame|center|200px|Animation of smallest positive frequency of Diels Alder transition state]]

[[Image:dielsalderbondlengths.jpg|frame|center|x400px|Image of Diels Alder Transition State with bond lengths indicated]]

Typical sp3 and sp2 C-C bond lengths are 1.5 Å and 1.3 Å. The bond lengths are around 1.4 Å which are in between, indicating that the π bonds are lengthening to form σ bonds and the σ bond is shortening to form a π bond.

With a van der Waals radius of the C atom of 1.7 Å <ref name="vdw">A. Bondi, ''J. Phys. Chem.'', '''1964''', ''68'', 441-451</ref>, the C-C bondlength of the partly formed C-C bond in the transition structure is much smaller than the sum of the two van der Waals radii but not small enough to be a C-C σ bond.

[[Image:dielsalderHOMO.jpg|frame|center|x400px|HOMO orbital of Diels Alder transition state]]

The HOMO was plotted and the HOMO is shown to be antisymmetric with respect to the plane. The HOMO involves the HOMO from butadiene and the LUMO from ethene. These molecular orbitals can interact because they are of the same symmetry (antisymmetric) and the mixing of these orbitals matches the shape of the HOMO.

[[File:DIELS_ALDER_BERNY_TSV2.LOG]]

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

[[Image:iiirxnscheme.jpg|frame|center|200px|Reaction scheme of Diels-Alder reaction involving maleic anhydride (dienophile) and hexadiene]]

The energies were calculated to be very close for the two products - the energy was taken to be -31.6 kcalmol-1 for both though if more decimal places were considered, exo was slightly higher in energy as expected. The close match in energies suggests that one of the transition states has not reached its minima however further optimisations using the same TS Berny method on the AM1 theory of calculation did not give closer results. Although the bonds appeared to be the correct bond order in the checkpoint files, upon investigation of the bond lengths it was found that the endo form was in fact the exo form. Attempts were made to optimise the endo form but each optimisation yielded the exo form and limited time was available when the error was discovered.

[[Image:exobondlengths.jpg|frame|center|x300px|Bond lengths of C-C bonds in the exo form]]

The bond lengths show the π bonds stretching to form σ bonds and the σ bond shortening to a π bond. The C-C bond forming distance between the two molecules is also shorter than the van der Waals radii to indicate the bond being formed. In the exo form, the distance between the (C)-O-(C) and the carbons opposite was 3.3 Å which is just slightly larger than the sum of their van der Waals radii (3.2 Å). A closer interaction would be sterically unfavourable.

[[Image:exo_TS.gif|frame|center|200px|Vibration frequency showing the bonds forming]]

[[Image:exoTSbernyv4LUMO.jpg|frame|center|x400px|LUMO of exo TS]]
[[Image:exoTSbernyv4HOMO.jpg|frame|center|x400px|HOMO of exo TS]]

The HOMO and LUMO were plotted which showed that both the molecular orbitals were antisymmetric. There was also a node between the -C(=O)-O-C(=O)- section and the rest of the molecule, indicating that this not part of the bond forming reaction pathway. If the endo had been successful, there may have been less of a separation between these molecular orbitals to favour the endo form over the exo form as a result of secondary molecular orbital interactions.

[[File:EXOPRODUCTTSBERNYV4.LOG]]

[[File:ENDOTSBERNYV1.LOG]]

<references/>

Rep:Mod:kitten

2014-03-21T16:25:17Z

Da1111:

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data. Calculations are shown in the log files provided.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. <ref name="cope">IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997) </ref> and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature <ref name="conf">B. W. Gung, Z. Zhu, and R. A. Fouch, ''J. Am. Chem. Soc.'', '''1995''', ''117'', 1783-1788</ref>
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

[[File:ANTICIATTEMPT2V3FREQ.LOG]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]
[[File:CHAIRTSGUESSV1IRCATTEMPT1.LOG]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

[[File:CHAIRTSGUESSV1REOPT.LOG]]
[[File:CHAIRTSGUESSV2CONTREOPT.LOG]]
[[File:BOATTSREOPTBERNY.LOG]]

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.<ref name="cope" />

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg|200px]] || [[Image:cisbutadiene_MO12.jpg|200px]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

[[File:CISBUTADIENE_OPT.LOG]]

===Transition State Geometry for Simple Diels-Alder Reaction===
The ethene MOs were also investigated and the symmetries reported in the table below.

{| class="wikitable" border="1"
|+ HOMO and LUMO of ethene
! !! HOMO !! LUMO
|-
| Image || [[Image:etheneHOMO.jpg|200px]] || [[Image:etheneLUMO.jpg|200px]]
|-
| Symmetry with respect to plane || symmetric || antisymmetric
|}

The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of 2.12 Å. An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at -956 cm-1 which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous and shows the reaction mechanism of the two molecules coming together, unlike the smallest positive frequency at 147 cm-1 which shows a rocking motion that could potentially result in asynchronous bond forming.

[[Image:Diels_alder_TS.gif|frame|center|200px|Animation of imaginary frequency of Diels Alder transition state<jmol><jmolAppletButton><uploadedFileContents>Diels_alder_berny_TSv2HOMO.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[Image:Diels_alder_TS_positive_frequency.gif|frame|center|200px|Animation of smallest positive frequency of Diels Alder transition state]]

[[Image:dielsalderbondlengths.jpg|frame|center|x400px|Image of Diels Alder Transition State with bond lengths indicated]]

Typical sp3 and sp2 C-C bond lengths are 1.5 Å and 1.3 Å http://books.google.co.uk/books?id=nacWAAAAQBAJ&pg=PA53&lpg=PA53&dq=sp3+C+bond+length&source=bl&ots=_uZLG60PZT&sig=oafat2pbjyU_QohC3uEXD6UEe1g&hl=en&sa=X&ei=hT4sU8zJMsOu7AbA94GYBA&ved=0CFYQ6AEwBQ#v=onepage&q=sp3%20C%20bond%20length&f=false The bond lengths are around 1.4 Å which are in between, indicating that the π bonds are lengthening to form σ bonds and the σ bond is shortening to form a π bond.

With a van der Waals radius of the C atom of 1.7 Å Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51, the C-C bondlength of the partly formed C-C bond in the transition structure is much smaller than the sum of the two van der Waals radii but not small enough to be a C-C σ bond.

[[Image:dielsalderHOMO.jpg|frame|center|x400px|HOMO orbital of Diels Alder transition state]]

The HOMO was plotted and the HOMO is shown to be antisymmetric with respect to the plane. The HOMO involves the HOMO from butadiene and the LUMO from ethene. These molecular orbitals can interact because they are of the same symmetry (antisymmetric) and the mixing of these orbitals matches the shape of the HOMO.

[[File:DIELS_ALDER_BERNY_TSV2.LOG]]

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

[[Image:iiirxnscheme.jpg|frame|center|200px|Reaction scheme of Diels-Alder reaction involving maleic anhydride (dienophile) and hexadiene]]

The energies were calculated to be very close for the two products - the energy was taken to be -31.6 kcalmol-1 for both though if more decimal places were considered, exo was slightly higher in energy as expected. The close match in energies suggests that one of the transition states has not reached its minima however further optimisations using the same TS Berny method on the AM1 theory of calculation did not give closer results. Although the bonds appeared to be the correct bond order in the checkpoint files, upon investigation of the bond lengths it was found that the endo form was in fact the exo form. Attempts were made to optimise the endo form but each optimisation yielded the exo form and limited time was available when the error was discovered.

[[Image:exobondlengths.jpg|frame|center|x300px|Bond lengths of C-C bonds in the exo form]]

The bond lengths show the π bonds stretching to form σ bonds and the σ bond shortening to a π bond. The C-C bond forming distance between the two molecules is also shorter than the van der Waals radii to indicate the bond being formed. In the exo form, the distance between the (C)-O-(C) and the carbons opposite was 3.3 Å which is just slightly larger than the sum of their van der Waals radii (3.2 Å). A closer interaction would be sterically unfavourable.

[[Image:exo_TS.gif|frame|center|200px|Vibration frequency showing the bonds forming]]

[[Image:exoTSbernyv4LUMO.jpg|frame|center|x400px|LUMO of exo TS]]
[[Image:exoTSbernyv4HOMO.jpg|frame|center|x400px|HOMO of exo TS]]

The HOMO and LUMO were plotted which showed that both the molecular orbitals were antisymmetric. There was also a node between the -C(=O)-O-C(=O)- section and the rest of the molecule, indicating that this not part of the bond forming reaction pathway. If the endo had been successful, there may have been less of a separation between these molecular orbitals to favour the endo form over the exo form as a result of secondary molecular orbital interactions.

[[File:EXOPRODUCTTSBERNYV4.LOG]]

[[File:ENDOTSBERNYV1.LOG]]

<references/>

Rep:Mod:kitten

2014-03-21T16:22:52Z

Da1111:

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data. Calculations are shown in the log files provided.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. <ref name="cope">IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997) </ref> and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature <ref name="conf">B. W. Gung, Z. Zhu, and R. A. Fouch, ''J. Am. Chem. Soc.'', '''1995''', ''117'', 1783-1788</ref>
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

[[File:ANTICIATTEMPT2V3FREQ.LOG]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]
[[File:CHAIRTSGUESSV1IRCATTEMPT1.LOG]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

[[File:CHAIRTSGUESSV1REOPT.LOG]]
[[File:CHAIRTSGUESSV2CONTREOPT.LOG]]
[[File:BOATTSREOPTBERNY.LOG]]

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg|200px]] || [[Image:cisbutadiene_MO12.jpg|200px]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

[[File:CISBUTADIENE_OPT.LOG]]

===Transition State Geometry for Simple Diels-Alder Reaction===
The ethene MOs were also investigated and the symmetries reported in the table below.

{| class="wikitable" border="1"
|+ HOMO and LUMO of ethene
! !! HOMO !! LUMO
|-
| Image || [[Image:etheneHOMO.jpg|200px]] || [[Image:etheneLUMO.jpg|200px]]
|-
| Symmetry with respect to plane || symmetric || antisymmetric
|}

The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of 2.12 Å. An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at -956 cm-1 which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous and shows the reaction mechanism of the two molecules coming together, unlike the smallest positive frequency at 147 cm-1 which shows a rocking motion that could potentially result in asynchronous bond forming.

[[Image:Diels_alder_TS.gif|frame|center|200px|Animation of imaginary frequency of Diels Alder transition state<jmol><jmolAppletButton><uploadedFileContents>Diels_alder_berny_TSv2HOMO.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[Image:Diels_alder_TS_positive_frequency.gif|frame|center|200px|Animation of smallest positive frequency of Diels Alder transition state]]

[[Image:dielsalderbondlengths.jpg|frame|center|x400px|Image of Diels Alder Transition State with bond lengths indicated]]

Typical sp3 and sp2 C-C bond lengths are 1.5 Å and 1.3 Å http://books.google.co.uk/books?id=nacWAAAAQBAJ&pg=PA53&lpg=PA53&dq=sp3+C+bond+length&source=bl&ots=_uZLG60PZT&sig=oafat2pbjyU_QohC3uEXD6UEe1g&hl=en&sa=X&ei=hT4sU8zJMsOu7AbA94GYBA&ved=0CFYQ6AEwBQ#v=onepage&q=sp3%20C%20bond%20length&f=false The bond lengths are around 1.4 Å which are in between, indicating that the π bonds are lengthening to form σ bonds and the σ bond is shortening to form a π bond.

With a van der Waals radius of the C atom of 1.7 Å Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51, the C-C bondlength of the partly formed C-C bond in the transition structure is much smaller than the sum of the two van der Waals radii but not small enough to be a C-C σ bond.

[[Image:dielsalderHOMO.jpg|frame|center|x400px|HOMO orbital of Diels Alder transition state]]

The HOMO was plotted and the HOMO is shown to be antisymmetric with respect to the plane. The HOMO involves the HOMO from butadiene and the LUMO from ethene. These molecular orbitals can interact because they are of the same symmetry (antisymmetric) and the mixing of these orbitals matches the shape of the HOMO.

[[File:DIELS_ALDER_BERNY_TSV2.LOG]]

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

[[Image:iiirxnscheme.jpg|frame|center|200px|Reaction scheme of Diels-Alder reaction involving maleic anhydride (dienophile) and hexadiene]]

The energies were calculated to be very close for the two products - the energy was taken to be -31.6 kcalmol-1 for both though if more decimal places were considered, exo was slightly higher in energy as expected. The close match in energies suggests that one of the transition states has not reached its minima however further optimisations using the same TS Berny method on the AM1 theory of calculation did not give closer results. Although the bonds appeared to be the correct bond order in the checkpoint files, upon investigation of the bond lengths it was found that the endo form was in fact the exo form. Attempts were made to optimise the endo form but each optimisation yielded the exo form and limited time was available when the error was discovered.

[[Image:exobondlengths.jpg|frame|center|x300px|Bond lengths of C-C bonds in the exo form]]

The bond lengths show the π bonds stretching to form σ bonds and the σ bond shortening to a π bond. The C-C bond forming distance between the two molecules is also shorter than the van der Waals radii to indicate the bond being formed. In the exo form, the distance between the (C)-O-(C) and the carbons opposite was 3.3 Å which is just slightly larger than the sum of their van der Waals radii (3.2 Å). A closer interaction would be sterically unfavourable.

[[Image:exo_TS.gif|frame|center|200px|Vibration frequency showing the bonds forming]]

[[Image:exoTSbernyv4LUMO.jpg|frame|center|x400px|LUMO of exo TS]]
[[Image:exoTSbernyv4HOMO.jpg|frame|center|x400px|HOMO of exo TS]]

The HOMO and LUMO were plotted which showed that both the molecular orbitals were antisymmetric. There was also a node between the -C(=O)-O-C(=O)- section and the rest of the molecule, indicating that this not part of the bond forming reaction pathway. If the endo had been successful, there may have been less of a separation between these molecular orbitals to favour the endo form over the exo form as a result of secondary molecular orbital interactions.

[[File:EXOPRODUCTTSBERNYV4.LOG]]

[[File:ENDOTSBERNYV1.LOG]]

<references/>

Rep:Mod:kitten

2014-03-21T16:04:19Z

Da1111: /* Part 2: The Diels Alder Cycloaddition */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data. Calculations are shown in the log files provided.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

[[File:ANTICIATTEMPT2V3FREQ.LOG]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]
[[File:CHAIRTSGUESSV1IRCATTEMPT1.LOG]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

[[File:CHAIRTSGUESSV1REOPT.LOG]]
[[File:CHAIRTSGUESSV2CONTREOPT.LOG]]
[[File:BOATTSREOPTBERNY.LOG]]

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg|200px]] || [[Image:cisbutadiene_MO12.jpg|200px]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

[[File:CISBUTADIENE_OPT.LOG]]

===Transition State Geometry for Simple Diels-Alder Reaction===
The ethene MOs were also investigated and the symmetries reported in the table below.

{| class="wikitable" border="1"
|+ HOMO and LUMO of ethene
! !! HOMO !! LUMO
|-
| Image || [[Image:etheneHOMO.jpg|200px]] || [[Image:etheneLUMO.jpg|200px]]
|-
| Symmetry with respect to plane || symmetric || antisymmetric
|}

The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of 2.12 Å. An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at -956 cm-1 which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous and shows the reaction mechanism of the two molecules coming together, unlike the smallest positive frequency at 147 cm-1 which shows a rocking motion that could potentially result in asynchronous bond forming.

[[Image:Diels_alder_TS.gif|frame|center|200px|Animation of imaginary frequency of Diels Alder transition state<jmol><jmolAppletButton><uploadedFileContents>Diels_alder_berny_TSv2HOMO.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[Image:Diels_alder_TS_positive_frequency.gif|frame|center|200px|Animation of smallest positive frequency of Diels Alder transition state]]

[[Image:dielsalderbondlengths.jpg|frame|center|x400px|Image of Diels Alder Transition State with bond lengths indicated]]

Typical sp3 and sp2 C-C bond lengths are 1.5 Å and 1.3 Å http://books.google.co.uk/books?id=nacWAAAAQBAJ&pg=PA53&lpg=PA53&dq=sp3+C+bond+length&source=bl&ots=_uZLG60PZT&sig=oafat2pbjyU_QohC3uEXD6UEe1g&hl=en&sa=X&ei=hT4sU8zJMsOu7AbA94GYBA&ved=0CFYQ6AEwBQ#v=onepage&q=sp3%20C%20bond%20length&f=false The bond lengths are around 1.4 Å which are in between, indicating that the π bonds are lengthening to form σ bonds and the σ bond is shortening to form a π bond.

With a van der Waals radius of the C atom of 1.7 Å Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51, the C-C bondlength of the partly formed C-C bond in the transition structure is much smaller than the sum of the two van der Waals radii but not small enough to be a C-C σ bond.

[[Image:dielsalderHOMO.jpg|frame|center|x400px|HOMO orbital of Diels Alder transition state]]

The HOMO was plotted and the HOMO is shown to be antisymmetric with respect to the plane. The HOMO involves the HOMO from butadiene and the LUMO from ethene. These molecular orbitals can interact because they are of the same symmetry (antisymmetric) and the mixing of these orbitals matches the shape of the HOMO.

[[File:DIELS_ALDER_BERNY_TSV2.LOG]]

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

[[Image:iiirxnscheme.jpg|frame|center|200px|Reaction scheme of Diels-Alder reaction involving maleic anhydride (dienophile) and hexadiene]]

The energies were calculated to be very close for the two products - the energy was taken to be -31.6 kcalmol-1 for both though if more decimal places were considered, exo was slightly higher in energy as expected. The close match in energies suggests that one of the transition states has not reached its minima however further optimisations using the same TS Berny method on the AM1 theory of calculation did not give closer results. Although the bonds appeared to be the correct bond order in the checkpoint files, upon investigation of the bond lengths it was found that the endo form was in fact the exo form. Attempts were made to optimise the endo form but each optimisation yielded the exo form and limited time was available when the error was discovered.

[[Image:exobondlengths.jpg|frame|center|x300px|Bond lengths of C-C bonds in the exo form]]

The bond lengths show the π bonds stretching to form σ bonds and the σ bond shortening to a π bond. The C-C bond forming distance between the two molecules is also shorter than the van der Waals radii to indicate the bond being formed. In the exo form, the distance between the (C)-O-(C) and the carbons opposite was 3.3 Å which is just slightly larger than the sum of their van der Waals radii (3.2 Å). A closer interaction would be sterically unfavourable.

[[Image:exo_TS.gif|frame|center|200px|Vibration frequency showing the bonds forming]]

[[Image:exoTSbernyv4LUMO.jpg|frame|center|x400px|LUMO of exo TS]]
[[Image:exoTSbernyv4HOMO.jpg|frame|center|x400px|HOMO of exo TS]]

The HOMO and LUMO were plotted which showed that both the molecular orbitals were antisymmetric. There was also a node between the -C(=O)-O-C(=O)- section and the rest of the molecule, indicating that this not part of the bond forming reaction pathway. If the endo had been successful, there may have been less of a separation between these molecular orbitals to favour the endo form over the exo form as a result of secondary molecular orbital interactions.

[[File:EXOPRODUCTTSBERNYV4.LOG]]

[[File:ENDOTSBERNYV1.LOG]]

File:ENDOTSBERNYV1.LOG

2014-03-21T16:00:48Z

Da1111: uploaded a new version of "File:ENDOTSBERNYV1.LOG"

File:EXOPRODUCTTSBERNYV4.LOG

2014-03-21T16:00:47Z

Da1111: uploaded a new version of "File:EXOPRODUCTTSBERNYV4.LOG"

Rep:Mod:kitten

2014-03-21T14:06:45Z

Da1111: /* Transition State Geometry for Simple Diels-Alder Reaction */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg|200px]] || [[Image:cisbutadiene_MO12.jpg|200px]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

===Transition State Geometry for Simple Diels-Alder Reaction===
The ethene MOs were also investigated and the symmetries reported in the table below.

{| class="wikitable" border="1"
|+ HOMO and LUMO of ethene
! !! HOMO !! LUMO
|-
| Image || [[Image:etheneHOMO.jpg|200px]] || [[Image:etheneLUMO.jpg|200px]]
|-
| Symmetry with respect to plane || symmetric || antisymmetric
|}

The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of 2.12 Å. An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at -956 cm-1 which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous and shows the reaction mechanism of the two molecules coming together, unlike the smallest positive frequency at 147 cm-1 which shows a rocking motion that is not part of the reaction mechanism.

[[Image:Diels_alder_TS.gif|frame|center|200px|Animation of imaginary frequency of Diels Alder transition state<jmol><jmolAppletButton><uploadedFileContents>Diels_alder_berny_TSv2HOMO.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[Image:Diels_alder_TS_positive_frequency.gif|frame|center|200px|Animation of smallest positive frequency of Diels Alder transition state]]

[[Image:dielsalderbondlengths.jpg|frame|center|x300px|Image of Diels Alder Transition State with bond lengths indicated]]

Typical sp3 and sp2 C-C bond lengths are 1.5 Å and 1.3 Å http://books.google.co.uk/books?id=nacWAAAAQBAJ&pg=PA53&lpg=PA53&dq=sp3+C+bond+length&source=bl&ots=_uZLG60PZT&sig=oafat2pbjyU_QohC3uEXD6UEe1g&hl=en&sa=X&ei=hT4sU8zJMsOu7AbA94GYBA&ved=0CFYQ6AEwBQ#v=onepage&q=sp3%20C%20bond%20length&f=false The bond lengths are around 1.4 Å which are in between, indicating that the π bonds are lengthening to form σ bonds and the σ bond is shortening to form a π bond.

With a van der Waals radius of the C atom of 1.7 Å Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51, the C-C bondlength of the partly formed C-C bond in the transition structure is much smaller than the sum of the two van der Waals radii but not small enough to be a C-C σ bond.

[[Image:dielsalderHOMO.jpg|frame|center|200px|HOMO orbital of Diels Alder transition state]]

The HOMO was plotted and the HOMO is shown to be the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

File:Dielsalderbondlengths.jpg

2014-03-21T13:52:47Z

Da1111:

Rep:Mod:kitten

2014-03-21T13:47:17Z

Da1111: /* Transition State Geometry for Simple Diels-Alder Reaction */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg|200px]] || [[Image:cisbutadiene_MO12.jpg|200px]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

===Transition State Geometry for Simple Diels-Alder Reaction===
The ethene MOs were also investigated and the symmetries reported in the table below.

{| class="wikitable" border="1"
|+ HOMO and LUMO of ethene
! !! HOMO !! LUMO
|-
| Image || [[Image:etheneHOMO.jpg|200px]] || [[Image:etheneLUMO.jpg|200px]]
|-
| Symmetry with respect to plane || symmetric || antisymmetric
|}

The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of 2.12 Å. An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at -956 cm-1 which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous and shows the reaction mechanism of the two molecules coming together, unlike the smallest positive frequency at 147 cm-1 which shows a rocking motion that is not part of the reaction mechanism.

[[Image:Diels_alder_TS.gif|frame|center|200px|Animation of imaginary frequency of Diels Alder transition state<jmol><jmolAppletButton><uploadedFileContents>Diels_alder_berny_TSv2HOMO.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[Image:Diels_alder_TS_positive_frequency.gif|frame|center|200px|Animation of smallest positive frequency of Diels Alder transition state]]

IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

Rep:Mod:kitten

2014-03-21T13:45:22Z

Da1111: /* Transition State Geometry for Simple Diels-Alder Reaction */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg|200px]] || [[Image:cisbutadiene_MO12.jpg|200px]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

===Transition State Geometry for Simple Diels-Alder Reaction===
The ethene MOs were also investigated and the symmetries reported in the table below.

{| class="wikitable" border="1"
|+ HOMO and LUMO of ethene
! !! HOMO !! LUMO
|-
| Image || [[Image:etheneHOMO.jpg|200px]] || [[Image:etheneLUMO.jpg|200px]]
|-
| Symmetry with respect to plane || symmetric || antisymmetric
|}

The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of 2.12 Å. An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at -956 cm-1 which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous and shows the reaction mechanism of the two molecules coming together, unlike the smallest positive frequency at 147 cm-1 which shows a rocking motion that is not part of the reaction mechanism.

[[Image:Diels_alder_TS.gif|frame|center|200px|Animation of imaginary frequency of Diels Alder transition state<jmol><jmolAppletButton><uploadedFileContents>Diels_Alder_berny_TSv2HOMO.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[Image:Diels_alder_TS_positive_frequency.gif|frame|center|200px|Animation of smallest positive frequency of Diels Alder transition state]]

IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

Rep:Mod:kitten

2014-03-21T13:43:22Z

Da1111: /* Part 2: The Diels Alder Cycloaddition */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg|200px]] || [[Image:cisbutadiene_MO12.jpg|200px]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

===Transition State Geometry for Simple Diels-Alder Reaction===
The ethene MOs were also investigated and the symmetries reported in the table below.

{| class="wikitable" border="1"
|+ HOMO and LUMO of ethene
! !! HOMO !! LUMO
|-
| Image || [[Image:etheneHOMO.jpg|200px]] || [[Image:etheneLUMO.jpg|200px]]
|-
| Symmetry with respect to plane || symmetric || antisymmetric
|}

The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of 2.12 Å. An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at -956 cm-1 which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous and shows the reaction mechanism of the two molecules coming together, unlike the smallest positive frequency at 147 cm-1 which shows a rocking motion that is not part of the reaction mechanism.

[[Image:Diels_Alder_TS.gif|frame|center|200px|Animation of imaginary frequency of Diels Alder transition state<jmol><jmolAppletButton><uploadedFileContents>Diels_Alder_berny_TSv2HOMO.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[Image:Diels_Alder_TS_positive_frequency.gif|frame|center|200px|Animation of smallest positive frequency of Diels Alder transition state

IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

Rep:Mod:kitten

2014-03-21T13:14:07Z

Da1111: /* Cis butadiene */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg|200px]] || [[Image:cisbutadiene_MO12.jpg|200px]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

===Transition State Geometry for Simple Diels-Alder Reaction===
The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of ... An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at ___ which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous, COMPARE TO SMALLEST POSITIVE FREQUENCY

IMAGE-GIF
IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

Rep:Mod:kitten

2014-03-21T13:13:25Z

Da1111: /* Cis butadiene */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane, which is as expected.

{| class="wikitable" border="1"
|+ HOMO and LUMO of cisbutadiene
! !! HOMO !! LUMO
|-
| Image || [[Image:cisbutadiene_MO11.jpg]] || [[Image:cisbutadiene_MO12.jpg]]
|-
| Symmetry with respect to plane || antisymmetric || symmetric
|}

===Transition State Geometry for Simple Diels-Alder Reaction===
The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of ... An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at ___ which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous, COMPARE TO SMALLEST POSITIVE FREQUENCY

IMAGE-GIF
IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

Rep:Mod:kitten

2014-03-21T13:06:25Z

Da1111: /* Part 2: The Diels Alder Cycloaddition */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

[[Image:DArxnscheme.jpg|frame|center|400px|Reaction Scheme of Diels Alder reaction]]

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane.

TABLE - images of HOMO and LUMO

===Transition State Geometry for Simple Diels-Alder Reaction===
The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of ... An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at ___ which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous, COMPARE TO SMALLEST POSITIVE FREQUENCY

IMAGE-GIF
IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

File:DArxnscheme.jpg

2014-03-21T13:05:13Z

Da1111:

Rep:Mod:kitten

2014-03-21T13:04:30Z

Da1111: /* Part 2: The Diels Alder Cycloaddition */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
A cycloaddition is defined in IUPAC as a reaction in which two or molecules with unsaturated bonds come together to form a cycloadduct. The Diels Alder reaction is an example of a (4+2) cycloaddition involving a diene and a dienophile.http://goldbook.iupac.org/C01496.html

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane.

TABLE - images of HOMO and LUMO

===Transition State Geometry for Simple Diels-Alder Reaction===
The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of ... An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at ___ which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous, COMPARE TO SMALLEST POSITIVE FREQUENCY

IMAGE-GIF
IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

Rep:Mod:kitten

2014-03-21T12:58:55Z

Da1111: /* Calculating the activation energies via 'chair' and 'boat' transition structures */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

Considering the energies of chair transition structures from different methods, the energies are close enough to consider the chair transition state in general. As both methods gave similar data, it can be assumed that this is an accurate representation of the chair transition state.

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental (at 0 K)
|-
| Chair || 45.7 || 44.7 || 34.1 || 33.2 || 33.5 ± 0.5
|-
| Boat || 55.6 || 54.8 || 42.0 || 41.3 || 44.7 ± 2.0
|}

From comparing the activation energies to the experimental values given in the appendix of the Y3 Physical Computational wiki, the results at the higher level of theory are close to the energies expected but are slightly out of the accepted range. This method does not consider factors like solvation which would affect the experimental result and could be the result of this small difference. The activation energies at HF/3-21G level of theory are well out of the accepted range but does show the expected trend that the chair has a lower activation energy than the boat.

==Part 2: The Diels Alder Cycloaddition==
The Diels-Alder ...

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane.

TABLE - images of HOMO and LUMO

===Transition State Geometry for Simple Diels-Alder Reaction===
The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of ... An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at ___ which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous, COMPARE TO SMALLEST POSITIVE FREQUENCY

IMAGE-GIF
IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

Rep:Mod:kitten

2014-03-21T12:15:28Z

Da1111: /* Calculating the activation energies via 'chair' and 'boat' transition structures */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations (Hartrees)
! !!colspan="2" | HF/3-21G !! colspan="2" | B3LYP/6-31G*
|-
| || Electronic and zero-point energies || Electronic and thermal energies || Electronic and zero-point energies || Electronic and thermal energies
|-
| Chair (from Berny TS) || -231.466701 || -231.461341 || -234.414929 || -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 || -231.461345 || -234.414934 || -234.409011
|-
| Boat || -231.450930 || -231.445301 || -234.402343 || -234.396008
|-
| Anti (Reactant) || -231.539539 || -231.532566 || -234.469212 || -234.461856
|-
|}

{| class="wikitable" border="1"
|+ Activation energies (kcalmol-1)
! Transition state structure !! HF/3-21G (0 K) || HF/3-21G (298.15 K) !! B3LYP/6-31G* (0 K)!! B3LYP/6-31G* (298.15 K) !! Experimental
|-
| Chair (Berny TS) ||
|-
| Chair (frozen coordinates) || cell
|-
| Boat ||
|}

==Part 2: The Diels Alder Cycloaddition==
The Diels-Alder ...

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane.

TABLE - images of HOMO and LUMO

===Transition State Geometry for Simple Diels-Alder Reaction===
The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of ... An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at ___ which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous, COMPARE TO SMALLEST POSITIVE FREQUENCY

IMAGE-GIF
IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

Rep:Mod:kitten

2014-03-21T12:00:03Z

Da1111: /* Anti-1,5-hexadiene with Ci symmetry */

==Introduction==

In this report, the transition structures were investigated for two pericyclic reactions: the Cope Rearrangement (Part 1) and the Diels-Alder cycloaddition (Part 2). These calculations were carried out using Gaussview and Gaussian using the following methods:
* HF/3-21G
* B3LYP/6-31G*
* AM1

In addition to showing the HOMO and LUMO surfaces of the transition structures, the reaction pathways and activation energies were investigated and compared to available experimental data.

==Part 1: The Cope Rearrangement==

(Tutorial section - have to include in write up, giving answers, documentation proof, discussion and how any problems encountered were solved.)

The Cope Rearrangement is defined in IUPAC as the [3,3] sigmatropic rearrangement of 1,5-diene. [REFERENCE IUPAC: http://goldbook.iupac.org/D01559.html) and a reaction scheme is shown below.

[[Image:Coperearrangementscheme.jpg|center|200px| ]]

In the following section, the lowest energy conformations (anti or gauche) and the transition state structures (chair or boat) for 1,5-hexadiene are investigated. The calculation methods used will be HF/3-21G at first then further calculated at a higher level of theory using B3LYP/6-31G*.

===Optimising the Reactants and Products===

====Anti-1,5-hexadiene====

[[Image:antihexadiene.jpg|thumb|100px|Structure of anti-1,5-hexadiene]]
[[Image:antinewman.jpg|thumb|50px|Newman (anti)]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>anti.mol</uploadedFileContents>
<text>Click here to load Jmol of anti-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

In Gaussview, the anti 1,5-hexadiene structure was drawn and cleaned. The molecule was then optimised using the Hartree-Fock calculation method and the 3-21G basis set. The energy energy is noted below along with the point group (after symmetrising the structure in Gaussview). This data corresponded in the appendix provided in the physical computational wiki page to identify the molecule as "anti1".

[[File:ANTI.LOG|right|Log file]]

====Gauche-1,5-hexadiene====

[[Image:gauchehexadiene.jpg|thumb|75px|Structure of gauche-1,5-hexadiene]]
[[Image:gauchenewman.jpg|thumb|50px|Newman (gauche)]]

The above method was repeated using the gauche 1,5-hexadiene structure and the energy was compared to the anti conformation in the table below. The data was compared with the data provided in the physical computational wiki page to suggest that the "gauche3" structure had been formed.

When considering sterics, it could be suggested that anti would be the lowest energy conformation but the gauche has a lower energy conformation as a result of favourable electronic factors. This is supported in literature by http://pubs.acs.org/doi/pdf/10.1021/ja00111a016
where a favourable interaction between the proton on the alkene and the π orbital is given as a possible explanation.

<jmol>
<jmolAppletButton>
<uploadedFileContents>bgauchev2.mol</uploadedFileContents>
<text>Click here to load Jmol of gauche-1,5-hexadiene</text>
</jmolAppletButton>
</jmol>

[[File:BGAUCHEV2.LOG|right]]

====Comparison of lowest energy conformations of 1,5-hexadiene====

{| class="wikitable" border="1"
! Conformation !! Energy (Hartrees) !! Point Group
|-
| Anti || -231.69260 || C2
|-
| Gauche || -231.69266 || C1
|}

The energy was found to be -231.69260 and the point group to be C2 therefore the molecule was identified as "anti1" in the appendix table provided which has very close agreement.

The energy was found to be -231.69266 and the point group to be C1 therefore the molecule was identified as "gauche3".

From comparing the above data, it would be assumed that the lowest energy conformation would be the gauche conformation and due to steric factors, it would be more favourable for the end groups to be leaning away from each other and the protons on the central atoms facing opposite directions.

These conditions appear to be satisfied by the "gauche3" structure identified above and further attempts gave the same structure after optimisation using HF/3-21G. This was confirmed by comparison to the structures in the appendix provided which indicated "gauche3" was the lowest energy conformation.

====Anti-1,5-hexadiene with Ci symmetry====
Another anti-1,5-hexadiene structure was drawn with Ci point group symmetry and optimised at the HF/3-21G level of theory. The energy values obtained held good agreement with the energy value given in the appendix and appeared to have the same structure as the structure in the appendix therefore this was optimised at a higher level of theory (B3LYP/6-31G*).

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticibeforereopt.mol</uploadedFileContents>
<text>Jmol of HF/3-21G optimised molecule</text>
</jmolAppletButton>
</jmol>

<jmol>
<jmolAppletButton>
<uploadedFileContents>anticiafterreopt.mol</uploadedFileContents>
<text>Jmol of B3LYP/6-31G* optimised molecule</text>
</jmolAppletButton>
</jmol>

{| class="wikitable" border="1"
|+ Comparison of energies and geometries for anti Ci structure
! Characteristic !! Data given in appendix !! HF/3-21G !! B3LYP/6-31G*
|-
| Energy (Hartrees) || -231.69254 || -231.69254 || -234.61170
|-
| Terminal C=C bond lengths (Å) || - || 1.316 || 1.334
|-
| =C-C- bond lengths (Å)|| - || 1.509 || 1.504
|-
| Central C-C bond lengths (Å) || - || 1.553 || 1.548
|-
| C=C-C dihedral angle (°) || - || 124.8 || 125.3
|-
| C-C-C dihedral angle (°) || - || 111.3 || 112.7
|}

[[Image:anticicomparisontopdown.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the top looking down (reoptimised on the left)]]
[[Image:anticicomparisonsideon.jpg|frame|center|250px|Comparison of the geometries of the Ci anti hexadiene from the side (reoptimised on the left)]]

There does not appear to be a significant difference in the geometry though the reoptimised structure contains longer C=C double bonds and shorter C-C bonds and larger dihedral angles yet the energies have changed by 1831.8 kcalmol-1 which is surprising given the comparably small difference in geometry.

A frequency calculation was then run in order to show the vibrations and a simulated infrared spectrum. Energies are also given that can be compared to experimental values (free energies, enthalpies and entropies). The values given are provided in the table below.

[[File:Ci_IR_spectrum.svg|thumb|100px|Simulated IR spectrum]]

{| class="wikitable" border="1"
|+ List of energies from anti Ci structure using B3LYP/6-31G* level
! !! Energy (kcal mol-1)
|-
| Sum of electronic and zero-point energies || -234.469212
|-
| Sum of electronic and thermal energies || -234.461856
|-
| Sum of electronic and thermal enthalpies || -234.460912
|-
| Sum of electronic and thermal free energies || -234.500822
|}

===Optimising the Transition Structures===
In this section, three methods for optimising the transition structure are explored:
* Computing the force constants (using TS Berny optimisation)
* Using the frozen coordinate method
* Using QST2

====The 'Chair' Transition Structure for 1,5-hexadiene====
The chair structure was drawn first by drawing a single allyl fragment and optimising using the HF/3-21G level of theory. Two of these optimised structures were then appended together then orientated in the chair transition state orientation. The distances between the terminal ends were set to 2.2Å apart.

This chair structure was optimised in using two of the above methods all under the Hartree Fock and default basis set 3-21G.

=====Computing the force constants (TS Berny optimisation)=====

An optimisation and frequency calculation was carried out for the chair transition structure by optimising to TS(Berny) instead of optimising to a minimum. The force constants were set to calculate once and an additional keyword Opt=NoEigen was added in order to stop the calculation failing if more than one imaginary frequency was detected. However, only one imaginary frequency was detected at 818 cm-1 which was as expected. The vibration is shown by the gif to be corresponding to the Cope rearrangement.

[[Image:chair_TS_vibration.gif|frame|center|200px|Animation of chair transition state (TS Berny optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:CHAIRTSGUESSV1.LOG]]

=====Using the frozen coordinate method=====

[[Image:chairTSguessv2cont.jpg|frame|center|x200px|Chair transition state (frozen coordinate optimisation)<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv2cont.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

Using the chair structure, the Redundant Coord Editor in Gaussview and new bond coordinate distances were added then frozen in separate inputs. The optimisation was then run as if it were to a minimum (ensuring that the Opt=ModRedundant was in the input line) in order to find the lowest energy structure for the unfrozen coordinates. After the optimisation had finished, the bonds that were previously frozen were selected in the Redundant Coord Editor and instead of Unidentified, Bond was chosen and Derivative instead of Add. A transition state optimisation was set up with the force constants set to Never so that calculation of the Hessian matrix is avoided.

[[File:CHAIRTSGUESSV2CONT.LOG]]

====The 'Boat' Transition Structure for 1,5-hexadiene====
=====Using the QST2 method=====

This method involves specifying the reactants and products for a reaction which is then used in the calculation to interpolate between the structures to locate the transition state structure. First of all, the boat structure was created by pasting the Ci structure into a window. This was copied and pasted into another window (in the same MolGroup) but with inversion so that the two geometries could be compared side by side (representing the reactant and the product). The atoms in the reactants and products were required to be labelled in the same way by opening View then Label then the Atom List in the Edit menu.

The job type was set to Opt+Freq and the transition structure was optimised to TS (QST2). However, this job did not run successfully. For both the product and reactant, the dihedral angles for the central four carbons were edited to 0° and the non-terminal three carbons' angles were set to 100°. The QST2 calculation was then run again to give the boat transition structure with one imaginary frequency at 840cm-1. This is due to the original reactant and product not resembling the boat transition structure sufficiently for a QST2 optimisation to be run (where the purpose of changing the angles was to make the reactant and product more 'boat'-like).

[[Image:boat_TS_vibration.gif|frame|center|200px|Animation of boat transition state (QST2 method)<jmol><jmolAppletButton><uploadedFileContents>boatTS.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]

[[File:BOATTS.LOG]]

====Intrinsic Reaction Coordinate method====
The IRC method shows the minimum energy path from a transition state to a local minimum by taking small steps towards a geometry where the gradient of the energy surface is the steepest. This method was carried out on the chair transition structure optimised using the method involving calculating force constants.

IRC was selected as the Job Type and the reaction coordinate was computed in the forward direction (as it is symmetrical) with force constants calculated always. The maximum number of points was set to 1000 to ensure that a minimum was reached.

The gif file shows the reaction pathway and the IRC plot is also shown, indicating that a minimum had been reached at 14 steps.

[[Image:chair_IRC_movie.gif|frame|center|200px|Animation of lowest energy pathway<jmol><jmolAppletButton><uploadedFileContents>chairTSguessv1IRCattempt1.mol</uploadedFileContents><text>Click here to load Jmol</text></jmolAppletButton></jmol>]]
[[File:chair_IRC.svg|frame|center]]

====Calculating the activation energies via 'chair' and 'boat' transition structures====
From this point, the level of theory used for calculations was increased to use the B3LYP/6-31G* level of theory (optimising to TS Berny) starting from the structures that had already been optimised by the HF/3-21G calculation method. These structures were compared and showed that (similar to the anti Ci structure in a previous section), the geometries did not appear to have changed significantly but there was a noticeable difference in the energies.

{| class="wikitable" border="1"
|+ Comparison of different levels of theory on energy calculations
! !!HF/3-21G !! B3LYP/6-31G*
|-
| || Electronic and zero-point energies | Electronic and thermal energies || Electronic and zero-point energies | Electronic and thermal energies ||
|-
| Chair (from Berny TS) || -231.466701 | -231.461341 || -234.414929 | -234.409009
|-
| Chair (from frozen coordinates) || -231.466705 | -231.461345 || -234.414934 | -234.409011
|-
| Boat || -231.450930 | -231.445301 || -234.402343 | -234.396008
|-
| Anti (Reactant) || -231.539539 | -231.532566 || -234.469212 | -234.461856
|-
|}

==Part 2: The Diels Alder Cycloaddition==
The Diels-Alder ...

All the following calculations were carried out at AM1 semi-empirical molecular orbital method.

===Cis butadiene===
The HOMO and LUMO of cis butadiene are shown below after optimisation to a minimum in Gausssian with their corresponding symmetries in relation to the plane.

TABLE - images of HOMO and LUMO

===Transition State Geometry for Simple Diels-Alder Reaction===
The transition structure was guessed by first drawing the product in Gaussview then removing the bonds that would be formed in the reaction to give the reactant. Different distances between the ethene and cis butadiene were trialled before a successful transition structure was calculated to give a distance of ... An opt+freq calculation was carried out using the TS Berny optimisation method. The frequency calculation showed a frequency at ___ which corresponded to the vibration shown in the gif file, confirming a transition structure for the Diels Alder reaction. This appears to be synchronous, COMPARE TO SMALLEST POSITIVE FREQUENCY

IMAGE-GIF
IMAGE-BOND DISTANCES

Typical sp3 and sp2 C-C bond lengths are... With a van der Waals radius of the C atom of ..., the C-C bondlength of the partly formed C-C bond in the transition structure is...

The HOMO and LUMO were plotted and the HOMO is shown to be... the HOMO involves the ... from butadiene and the ... from ethene. This reaction is allowed because ...
IMAGE- HOMO AND LUMO

===Regioselectivity of the Diels-Alder Reaction===
In this section, the transition structure was investigated for the endo and exo adducts of cyclohexa-1,3-diene and maleic anhydride. The endo is the favoured product due to mainly kinetic control so the exo product is predicted to have the higher energy transition state.

TABLE - ENERGIES, BOND LENGTHS

Structural differences - why is exo more strained?

The HOMO was plotted which showed ... Nodal properties of HOMO between O=C-O-C=O and rest of system (secondary orbital overlap effect)

Rep:Mod:kitten

2014-03-21T11:27:03Z

Da1111: /* Gauche-1,5-hexadiene */

Rep:Mod:kitten

2014-03-21T11:26:22Z

Da1111: /* Anti-1,5-hexadiene */

Rep:Mod:kitten

2014-03-21T11:25:38Z

Da1111: /* Optimising the Reactants and Products */